| Zadanie 1 | ||||||||
| Rozwiązac zadanie umieszczone w arkuszu | 32 | A | ||||||
| Zadanie 2 | ||||||||
| Dane są dwa procesy Yt, Xt zamieszczone w arkuszu | 32 | oraz pewne informacje dotyczące struktury wewnętrznej | ||||||
| Uzupełnić informacje dotyczące wewnętrznej struktury procesów, tzn.: | ||||||||
| (z pominięciem ostatnich dwu obserwacji!). | ||||||||
| 1 | Zbadać stopień wielomianu trendu. | |||||||
| Odpowiedź uzasadnić. | ||||||||
| Napisać postać wybranego modelu trendu. | ||||||||
| 2 | Zbadać czy występuje sezonowość. | |||||||
| Odpowiedź uzasadnić. | ||||||||
| Jeśli sezonowość występuje, to podać interpretacje jednego wybranego współczynnika sezonowości. | ||||||||
| 3 | Zbadać rząd autoregresji. | |||||||
| Odpowiedź uzasadnić. | ||||||||
| W oparciu o informacje dotyczące wewnętrznych struktur procesów Yt oraz Xt, | ||||||||
| napisać hipotezę modelu zgodnego opisującego zależność Yt od Xt. | ||||||||
| Oszacować model zgodny wykorzystując MNK oraz usunąć nieistotne zmienne metodę eliminacji a posteriori. | ||||||||
| (z pominięciem ostatnich dwu obserwacji!). | ||||||||
| Dokonaj oceny jakości modelu oraz przydatności prognostycznej modelu. | ||||||||
| Podać interpretację ocen parametrów modelu zgodnego. | ||||||||
| Następnie wyznaczyć wartości prognozy wygasłej Yt na dwa okresy w przód | ||||||||
| oraz ocenić jakość otrzymanych prognoz, tzn.: | ||||||||
| 1 | Czy prognozy są dopuszczalne czy niedopuszczalne? | |||||||
| Odpowiedź uzasadnić. | ||||||||
| 2 | Czy prognozy są przeszacowane czy niedoszacowane? | |||||||
| Odpowiedź uzasadnić. | ||||||||
| 3 | Czy prognozy są trafne czy nietrafne? | |||||||
| Odpowiedź uzasadnić. | ||||||||
| 4 | Podać interpretację błędu ex ante. |
| Yt | Xt | dane kwartalne | ||||
| 212,2817 | 163,9990 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 213,6472 | 164,4256 | Yt | ||||
| 216,9971 | 167,3392 | Xt | 2 | - | 2 | |
| 217,050184185672 | 169,578659328715 | |||||
| 218,342586206751 | 170,045317892187 | |||||
| 221,577677132242 | 171,993027003826 | |||||
| 222,837226337875 | 175,366689045421 | |||||
| 223,043292220443 | 176,309902625722 | |||||
| 226,885803432423 | 178,959665957265 | |||||
| 225,906804488931 | 178,46923852407 | |||||
| 228,399130979216 | 178,546276731536 | |||||
| 229,468731621371 | 183,268870629294 | |||||
| 230,939903995843 | 185,913511684962 | |||||
| 232,194953456311 | 187,32415875926 | |||||
| 233,165382329126 | 187,619890581571 | |||||
| 235,72755394179 | 190,889270845239 | |||||
| 239,697712396842 | 192,061906274515 | |||||
| 239,541297343099 | 193,810035426613 | |||||
| 240,849419187977 | 197,246558746162 | |||||
| 240,733330445974 | 199,520321077052 | |||||
| 241,795019527607 | 200,234469147766 | |||||
| 242,132869005782 | 201,026353057839 | |||||
| 244,270808326229 | 203,125524175597 | |||||
| 247,986559760327 | 205,906473282223 | |||||
| 249,921098709155 | 208,445274299095 | |||||
| 250,216818413088 | 206,792775266568 | |||||
| 252,706843110053 | 208,408455440303 | |||||
| 254,733089273728 | 213,359163157555 | |||||
| 258,201561706681 | 218,324015718412 | |||||
| 259,03854900775 | 219,533744168025 | |||||
| 259,616108568594 | 218,37754021345 | |||||
| 261,474032461365 | 220,89052646086 | |||||
| 263,004334511035 | 224,706299791136 | |||||
| 267,076226952902 | 226,964669290337 | |||||
| 267,983886982741 | 229,524881657748 | |||||
| 266,45175371619 | 230,886061278514 | |||||
| 266,883703590471 | 231,788484104009 | |||||
| 268,173413744733 | 231,687565951 | |||||
| 270,769588349115 | 234,727945928996 | |||||
| 272,832678280807 | 237,831541176998 | |||||
| 276,290077013454 | 240,3566463346 | |||||
| 276,985412588058 | 242,500671329961 | |||||
| 279,134460593607 | 244,457044264137 | |||||
| 280,916748244018 | 247,262558026497 | |||||
| 281,290893170507 | 248,623317110244 | |||||
| 280,273350835466 | 248,700467055547 | |||||
| 282,913885348462 | 251,169253389231 | |||||
| 285,248661932583 | 255,20146521132 | |||||
| 285,518103549011 | 256,416277771099 | |||||
| 289,055172620797 | 258,478180578132 | |||||
| 290,961539785085 | 261,440997238439 | |||||
| 293,202233638838 | 264,377226111811 | |||||
| 294,389328677322 | 266,840036771711 | |||||
| 296,036470954884 | 268,306631618302 | |||||
| 296,434759704015 | 271,881564262297 | |||||
| 297,968181741462 | 273,022385910057 | |||||
| 299,608497313774 | 274,986605841116 | |||||
| 302,364301766932 | 277,523409140646 | |||||
| 305,571600172275 | 280,842203147942 | |||||
| 306,708028415405 | 282,580958232506 | |||||
| 308,77817148974 | 285,346793680327 | |||||
| 311,545133782385 | 286,818692915194 | |||||
| 314,682242800887 | 288,983498276985 | |||||
| 315,533707731254 | 291,521521800114 | |||||
| 318,088230300236 | 295,122313769274 | |||||
| 319,049126478559 | 296,608179541519 | |||||
| 319,6040094625 | 299,841182217202 | |||||
| 322,527327933807 | 302,185237513714 | |||||
| 324,537089399149 | 303,823869621347 | |||||
| 326,577740677899 | 305,410126767323 | |||||
| 329,774352753046 | 307,479028211855 | |||||
| 331,221202433651 | 310,631566220184 | |||||
| 333,474773885464 | 314,708528447368 | |||||
| 334,658600121064 | 317,506290580347 | |||||
| 336,538058900075 | 317,312862969261 | |||||
| 337,577214482431 | 320,807001549418 | |||||
| 339,289134724834 | 323,352955741946 | |||||
| 341,808564839631 | 324,926072825401 | |||||
| 341,627844912696 | 326,222961398462 | |||||
| 342,449705961191 | 329,111447708917 | |||||
| 345,399333086349 | 332,475284065965 | |||||
| 348,660441204689 | 336,938991356012 | |||||
| 347,582863356952 | 338,087181187221 | |||||
| 350,236092466635 | 340,042112169928 | |||||
| 354,242815604369 | 343,700194827068 | |||||
| 357,216845109553 | 345,71777202827 | |||||
| 357,832622190776 | 347,606685286135 | |||||
| 359,858140954041 | 350,516002360373 | |||||
| 360,628283537812 | 352,30782730177 | |||||
| 363,39388266192 | 355,133195436913 | |||||
| 365,367985642452 | 359,43488634144 | |||||
| 367,685798050915 | 361,346253630099 | |||||
| 368,632234438675 | 362,629397641483 | |||||
| 370,788036375392 | 366,730537132851 | |||||
| 371,305965516042 | 368,923763223117 | |||||
| 373,398963492607 | 371,33064308073 | |||||
| 373,728761255716 | 374,122680559191 | |||||
| 377,646036039672 | 377,096451103223 | |||||
| 379,719504463159 | 379,766798438257 |
| Zadanie |
| Dokaonaj identyfikacji modelu ARMA (do p=3 i q=3) dla poniższego szeregu |
| Yt |
| 0,63527413 |
| -0,093192818 |
| 0,47663046 |
| -0,71853609 |
| -0,48883828 |
| -2,3956339 |
| -2,4095951 |
| -1,465628 |
| -1,4935071 |
| 0,041749948 |
| -0,5978797 |
| -2,8035149 |
| -3,4744484 |
| -1,7239104 |
| -1,4923523 |
| -0,8146582 |
| 0,29247316 |
| -1,8864482 |
| -2,1538374 |
| -2,4273717 |
| -2,9600346 |
| -2,5501095 |
| -0,51907438 |
| -0,45369826 |
| 0,86448938 |
| -0,0046132978 |
| 0,0038338483 |
| -0,77982597 |
| -0,036922213 |
| -0,28074515 |
| 0,25553971 |
| 0,8725868 |
| 0,61974824 |
| 1,3849712 |
| 3,4172645 |
| 3,2584502 |
| 2,5949729 |
| 2,9891191 |
| 2,447236 |
| 0,85071888 |
| 1,1660728 |
| 0,92785318 |
| 0,46606468 |
| 1,6493042 |
| 3,182844 |
| 2,0237159 |
| 1,7223972 |
| 0,5702686 |
| 1,1366535 |
| -1,4552671 |
| -0,17409879 |
| 0,079620088 |
| 0,32535853 |
| 1,4737313 |
| 0,90431807 |
| 0,59032 |
| -0,7982442 |
| -2,3022018 |
| -2,5453157 |
| -1,7553721 |
| -1,945507 |
| -2,8899363 |
| -1,2392628 |
| -1,7034957 |
| -1,3740821 |
| -1,1000827 |
| -1,1295025 |
| -0,50702665 |
| -0,66963467 |
| -2,1997186 |
| -2,78875 |
| -1,9879053 |
| -2,8469143 |
| -2,6247147 |
| -3,0411439 |
| -3,6074754 |
| -3,907122 |
| -3,5273644 |
| -2,6482258 |
| -2,2346991 |
| -0,72364017 |
| -0,82429843 |
| -2,1769779 |
| -1,7318481 |
| -1,3141056 |
| -0,7347487 |
| -0,087973296 |
| 1,2077055 |
| 0,41834826 |
| 0,59548701 |
| 0,46321293 |
| -0,20969365 |
| 1,9685535 |
| 1,3172257 |
| -0,35574794 |
| 1,4855025 |
| 1,513948 |
| 0,092118837 |
| 0,69404521 |
| 1,825018 |
| 0,56397191 |
| 0,58635297 |
| 0,33004237 |
| -0,8993614 |
| 0,46423042 |
| 0,35595467 |
| 0,82098243 |
| -0,059642677 |
| -0,70327353 |
| -0,24825606 |
| -0,091790773 |
| 1,7747836 |
| 1,1447212 |
| 3,128331 |
| 4,0111906 |
| 1,2638739 |
| -0,66944368 |
| -1,1090891 |
| -1,0730878 |
| -0,84953612 |
| 0,157321 |
| -0,59641387 |
| -1,1986216 |
| -1,1600783 |
| -0,94852677 |
| -0,47993142 |
| 0,67434968 |
| 1,161153 |
| -0,82169287 |
| 0,039993259 |
| 0,84348047 |
| 1,3111293 |
| 2,3589838 |
| 2,2142846 |
| 1,0984345 |
| 0,72942009 |
| -1,8654817 |
| -1,0190997 |
| -0,69833413 |
| -1,1497711 |
| -1,5745246 |
| -2,3402815 |
| -1,9199561 |
| -1,1566203 |
| -1,2556573 |
| -1,5044241 |
| -1,2395179 |
| -1,1663746 |
| -1,8903648 |
| -0,21974393 |
| 0,2651145 |
| 1,4930325 |
| 0,69669623 |
| -0,56135966 |
| 0,35856189 |
| 0,32804909 |
| -0,49376933 |
| -0,48414461 |
| -2,396166 |
| -0,83301477 |
| -1,6476024 |
| -2,0065705 |
| -0,26577695 |
| -1,1218647 |
| -1,3103495 |
| -1,5544428 |
| 0,37619357 |
| 0,38185556 |
| -0,77557204 |
| -1,7449754 |
| 0,33969599 |
| 2,2092154 |
| 3,4024405 |
| 1,4660123 |
| 0,9592723 |
| 0,56848579 |
| 0,76228781 |
| 0,037504792 |
| -0,94764453 |
| -1,204925 |
| 0,11815187 |
| 2,4671694 |
| 2,2030239 |
| 1,495796 |
| 1,898309 |
| 1,0310567 |
| 2,6873251 |
| 3,2567112 |
| 1,3778032 |
| 0,43235746 |
| 1,6868154 |
| 1,7375357 |
| 1,7830874 |
| -0,28086362 |
| 0,00316775 |
| 0,68816706 |
| -0,086256467 |
| -1,0716107 |
| -1,0429093 |
| -1,8883601 |
| Yt | Xt | dane miesięczne | ||||
| 90,0250 | 42,7575 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 89,8116 | 41,9237 | Yt | 1 | - | 1 | |
| 90,6163 | 41,8935 | Xt | ||||
| 92,4503 | 42,2847 | |||||
| 93,8524 | 43,3356 | |||||
| 95,1314 | 45,8227 | |||||
| 95,5054 | 46,9733 | |||||
| 95,9269 | 46,6956 | |||||
| 99,1617 | 47,3181 | |||||
| 98,7158 | 47,6004 | |||||
| 100,9744 | 48,5589 | |||||
| 101,0647 | 47,5037 | |||||
| 101,7103 | 49,5558 | |||||
| 102,9806 | 50,4912 | |||||
| 105,6941 | 53,1088 | |||||
| 106,9595 | 53,5790 | |||||
| 109,7527 | 53,2400 | |||||
| 109,2529 | 54,6855 | |||||
| 109,7150 | 58,0843 | |||||
| 110,5359 | 56,8902 | |||||
| 111,2905 | 56,9464 | |||||
| 111,3144 | 55,3884 | |||||
| 111,6414 | 56,5548 | |||||
| 112,8949 | 59,2539 | |||||
| 114,6376 | 61,3476 | |||||
| 115,3661 | 61,4914 | |||||
| 118,4073 | 63,2857 | |||||
| 117,8342 | 63,1905 | |||||
| 121,0833 | 64,1292 | |||||
| 119,3797 | 65,2445 | |||||
| 121,5440 | 66,9503 | |||||
| 121,6045 | 68,1294 | |||||
| 120,4063 | 68,1352 | |||||
| 124,8770 | 70,6491 | |||||
| 126,4348 | 70,0746 | |||||
| 127,3201 | 72,7491 | |||||
| 127,6568 | 72,3706 | |||||
| 129,2325 | 71,7236 | |||||
| 129,2959 | 71,6591 | |||||
| 130,1018 | 73,8113 | |||||
| 132,6342 | 77,4362 | |||||
| 134,0370 | 78,7596 | |||||
| 136,9524 | 81,5928 | |||||
| 137,0238 | 81,0498 | |||||
| 137,1687 | 80,6915 | |||||
| 137,6736 | 81,9767 | |||||
| 138,7167 | 83,4875 | |||||
| 140,6320 | 87,1484 | |||||
| 143,1490 | 86,6487 | |||||
| 143,9786 | 87,1416 | |||||
| 145,2504 | 87,1577 | |||||
| 146,8162 | 87,8008 | |||||
| 148,2349 | 91,1971 | |||||
| 150,3323 | 91,2379 | |||||
| 149,2086 | 91,2380 | |||||
| 150,6621 | 92,9741 | |||||
| 153,1830 | 97,4478 | |||||
| 154,5523 | 99,2814 | |||||
| 154,3586 | 99,2338 | |||||
| 156,7992 | 100,3557 | |||||
| 157,3404 | 100,6784 | |||||
| 156,4644 | 101,7291 | |||||
| 158,9675 | 102,0265 | |||||
| 160,5590 | 103,7198 | |||||
| 161,7371 | 107,0577 | |||||
| 162,7736 | 108,2851 | |||||
| 165,4424 | 110,2430 | |||||
| 165,5135 | 110,0603 | |||||
| 164,8496 | 109,6111 | |||||
| 166,5623 | 111,9218 | |||||
| 170,3065 | 114,2473 | |||||
| 172,7314 | 116,6598 | |||||
| 171,3639 | 119,4774 | |||||
| 172,7513 | 119,9598 | |||||
| 173,1511 | 120,1555 | |||||
| 175,6583 | 120,8930 | |||||
| 176,3036 | 123,3388 | |||||
| 179,3807 | 125,6568 | |||||
| 180,3143 | 125,9289 | |||||
| 183,5868 | 129,1918 | |||||
| 185,3430 | 129,1663 | |||||
| 185,4878 | 130,5802 | |||||
| 186,7403 | 131,6943 | |||||
| 187,5569 | 134,4845 | |||||
| 188,8683 | 136,4607 | |||||
| 190,4373 | 139,2393 | |||||
| 191,5073 | 137,4137 | |||||
| 194,7457 | 140,0178 | |||||
| 194,6066 | 143,1898 | |||||
| 196,2274 | 146,1994 | |||||
| 196,0845 | 145,4973 | |||||
| 195,8997 | 145,8829 | |||||
| 199,6674 | 148,8382 | |||||
| 201,0498 | 150,5648 | |||||
| 202,9924 | 151,5507 | |||||
| 204,8309 | 154,4447 | |||||
| 206,9900 | 156,8789 | |||||
| 207,8300 | 156,8681 | |||||
| 209,9599 | 159,0477 | |||||
| 208,7891 | 160,2760 |
| Zadanie |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich dwóch obserwacji) |
| dokonać wyrównania wykładniczego |
| oraz wyrównać szereg za pomocą sredniej 3-wyrazowj. |
| Obliczyć prognozy. Która metoda dała lepsze wyniki? |
| Pt |
| 17,6 |
| 17,4 |
| 16,9 |
| 17,45 |
| 15,8 |
| 15,8 |
| 15,65 |
| 15,8 |
| 15,7 |
| 16,75 |
| 16,1 |
| 16 |
| 17,1 |
| 16,45 |
| 17,7 |
| 18,05 |
| 18,35 |
| 19,05 |
| 19,75 |
| 21,8 |
| 23,5 |
| 22,9 |
| 21,4 |
| 23 |
| 26 |
| 31 |
| 35 |
| 32,1 |
| 31,2 |
| 27,6 |
| 32,2 |
| 30,6 |
| 29 |
| 28,3 |
| 28,2 |
| 28,7 |
| 28,2 |
| 28,1 |
| 29,5 |
| 29,4 |
| 29,3 |
| 28,4 |
| 26,7 |
| 27,8 |
| 22,7 |
| 22 |
| 22,5 |
| 19,3 |
| 19,95 |
| 21,9 |
| Yt | Xt | dane miesięczne | ||||
| 385,054086209856 | 384,826219797696 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 387,01502437048 | 389,032672429952 | Yt | 1 | - | ||
| 389,385751847198 | 392,951215538892 | Xt | 2 | |||
| 391,353502214553 | 394,896260351355 | |||||
| 391,896821017066 | 397,862869995256 | |||||
| 395,014101938025 | 401,555217856612 | |||||
| 397,143737862792 | 403,197182715865 | |||||
| 418,343839766552 | 431,014378465712 | |||||
| 418,262887365483 | 434,633924197271 | |||||
| 419,939164199463 | 437,870603132078 | |||||
| 444,35687602458 | 471,98367408889 | |||||
| 446,893720865277 | 475,14320275042 | |||||
| 472,014695790816 | 510,779201874849 | |||||
| 474,038911759648 | 515,652528665905 | |||||
| 477,478041938149 | 518,167036449603 | |||||
| 479,538567058374 | 521,9472104034 | |||||
| 481,235186759436 | 525,885011662199 | |||||
| 481,446201882148 | 527,760122835959 | |||||
| 485,012654750432 | 531,045569036696 | |||||
| 488,466781259859 | 535,426492287634 | |||||
| 491,154101436972 | 539,619067757902 | |||||
| 493,137205648854 | 541,712643739688 | |||||
| 495,344221459831 | 544,547559140652 | |||||
| 497,323859939011 | 547,002077988516 | |||||
| 497,982972040801 | 550,075323136849 | |||||
| 499,62223657954 | 552,838762686703 | |||||
| 504,410691796735 | 558,235328357282 | |||||
| 508,544809778891 | 561,449991939688 | |||||
| 510,790038814974 | 563,7626638209 | |||||
| 511,362004210594 | 566,459101516665 | |||||
| 511,93337441695 | 567,733495381639 | |||||
| 514,906241674224 | 569,762056622317 | |||||
| 515,6931745919 | 575,375735820735 | |||||
| 520,242962762523 | 580,570618843514 | |||||
| 522,97186515929 | 585,266276977814 | |||||
| 523,547072659833 | 588,582218649283 | |||||
| 527,658141866818 | 592,620720398444 | |||||
| 527,283013223475 | 593,860444779353 | |||||
| 528,253334771016 | 596,341678708235 | |||||
| 530,555362365049 | 599,382629313199 | |||||
| 533,174776906538 | 603,637306104626 | |||||
| 534,84457789586 | 606,007831937496 | |||||
| 539,63901932388 | 610,542176720647 | |||||
| 541,842002110473 | 612,06827325739 | |||||
| 544,351379373977 | 617,361093266175 | |||||
| 546,563789698819 | 622,328746656749 | |||||
| 548,702863529012 | 624,362910687579 | |||||
| 549,614527967535 | 625,140047749848 | |||||
| 554,661334233744 | 629,042164374877 | |||||
| 555,966665785646 | 633,945879524987 | |||||
| 559,769343994097 | 639,150161965041 | |||||
| 562,360504190303 | 643,20474536903 | |||||
| 564,803956970595 | 645,186982435402 | |||||
| 564,770028533262 | 647,424191313629 | |||||
| 568,238027345232 | 651,551721814017 | |||||
| 572,455811500591 | 656,436456562959 | |||||
| 573,48573421564 | 660,258485212168 | |||||
| 575,991600055837 | 662,892708502118 | |||||
| 577,949288410591 | 666,974531016403 | |||||
| 581,025879055692 | 671,394135208995 | |||||
| 584,345890085015 | 675,840168718836 | |||||
| 583,60722643665 | 678,791647147703 | |||||
| 585,736261831943 | 681,085920801088 | |||||
| 589,534697526485 | 685,012893621571 | |||||
| 591,320609284104 | 688,954367852508 | |||||
| 594,964044310363 | 693,481263262876 | |||||
| 596,505261747824 | 696,429110816723 | |||||
| 597,907933762173 | 699,128561184883 |
| Zadanie |
| Oblicz prognozę na okres 26, 27, 28 z najlepszego modelu średniej ruchomej (2, 3, 6- wyrazowej). |
| Policz błedy ex post. |
| Yt |
| 13170 |
| 13394 |
| 13425 |
| 27083 |
| 12402 |
| 10896 |
| 13701 |
| 25131 |
| 15715 |
| 14366 |
| 16031 |
| 27594 |
| 17977 |
| 16236 |
| 17907 |
| 28474 |
| 15567 |
| 16301 |
| 18270 |
| 31841 |
| 17972 |
| 16306 |
| 20492 |
| 33019 |
| 25583 |
| 22175 |
| 23785 |
| 34410 |
| Yt | Xt | dane kwartalne | ||||
| 24,409514549848 | 37,6239 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 19,9700573002599 | 33,4510 | Yt | 0 | + | 1 | |
| 37,3576115348788 | 45,6512 | Xt | ||||
| 28,6126288445955 | 40,3596285362865 | |||||
| 24,1706358303795 | 36,689723108206 | |||||
| 22,0830548131679 | 34,1377868716091 | |||||
| 37,033511395401 | 46,26166334817 | |||||
| 28,3476367882066 | 40,5004894487435 | |||||
| 26,8027208072648 | 39,3146352993753 | |||||
| 20,6949991789903 | 33,8289953446142 | |||||
| 37,2642564770508 | 44,0392899068324 | |||||
| 29,047808139859 | 40,5031454876087 | |||||
| 23,8113428963893 | 37,0415751956921 | |||||
| 20,1345437385441 | 34,6246307823314 | |||||
| 35,7699006396059 | 44,5924219305847 | |||||
| 29,9584694475673 | 41,4305273539118 | |||||
| 27,8235164268122 | 36,9624168350562 | |||||
| 22,0901868630302 | 34,7097239210903 | |||||
| 35,9862853124156 | 46,7167539323887 | |||||
| 27,4487571488515 | 42,2518861687491 | |||||
| 23,8529714575371 | 38,944113096748 | |||||
| 19,6450554738917 | 35,4774829221958 | |||||
| 35,6969718662921 | 46,3858464485921 | |||||
| 30,5386500025094 | 41,5606301264644 | |||||
| 26,3575031603121 | 38,9032354260171 | |||||
| 20,723049510908 | 32,5701610038311 | |||||
| 36,9837663396406 | 43,7068412048109 | |||||
| 29,1357017715784 | 39,4787059388325 | |||||
| 25,9226582302985 | 38,7201437239766 | |||||
| 21,6268664615697 | 35,9023297750735 | |||||
| 37,313126971346 | 46,0475997944706 | |||||
| 30,8774551870804 | 42,2377300644091 | |||||
| 25,8207362733798 | 39,9024520219719 | |||||
| 23,9808168933452 | 37,1933702736118 | |||||
| 39,1954324557236 | 49,4428117578768 | |||||
| 28,7757963340824 | 44,2492077324152 | |||||
| 23,7678619396222 | 40,9254941120898 | |||||
| 20,3842567492195 | 35,6833964354031 | |||||
| 37,1136076184475 | 47,0916445483858 | |||||
| 29,5431881819229 | 41,3097068372344 | |||||
| 26,6296830556969 | 38,6245381797758 | |||||
| 21,340784677528 | 35,6936060493586 | |||||
| 37,0096642801967 | 46,983883716101 | |||||
| 30,287594482948 | 42,9151044085131 | |||||
| 24,9560857416711 | 39,3091065500664 | |||||
| 18,5507431487088 | 34,8437185093736 | |||||
| 35,0442918115629 | 45,8492421889415 | |||||
| 28,6091965669708 | 41,3939395561637 | |||||
| 22,9278289668591 | 37,0684926885059 | |||||
| 20,7532013392425 | 34,6434290421644 | |||||
| 36,3297522219984 | 45,9474173206177 | |||||
| 29,4184159570901 | 41,7966805673187 | |||||
| 24,5897953682134 | 39,4066477281437 | |||||
| 20,6461487566125 | 36,3600093429583 | |||||
| 35,0542371509295 | 49,2472638107543 | |||||
| 27,9730749249697 | 43,0401315437114 | |||||
| 24,6814341460988 | 40,8070562008614 | |||||
| 21,4132873092233 | 37,5402204214794 | |||||
| 38,089825192351 | 49,6240228044038 | |||||
| 30,1372757206708 | 43,9850685689138 | |||||
| 26,0772808847252 | 42,2043038983736 | |||||
| 22,8987245142833 | 38,2012983488175 | |||||
| 40,0286573757733 | 49,6390564650198 | |||||
| 31,5127008840488 | 44,3348626039824 | |||||
| 27,306137417151 | 42,5701748321319 | |||||
| 22,4297679444004 | 38,6071523874699 | |||||
| 37,0683617939467 | 51,368571361325 | |||||
| 31,2598159545285 | 46,0060535666096 | |||||
| 28,238206517465 | 43,1449730708693 | |||||
| 24,256984542289 | 39,4099856402395 | |||||
| 40,6308389931945 | 49,9497725920825 | |||||
| 32,5883937455817 | 45,0570646331475 | |||||
| 27,9438543310391 | 43,2213734294654 | |||||
| 23,1938976836124 | 40,726788929207 | |||||
| 39,6553285520827 | 50,1785724597343 | |||||
| 32,4345773379994 | 46,9517054687096 | |||||
| 27,324832598123 | 42,8681372333047 | |||||
| 24,2481321027054 | 39,5407794886488 | |||||
| 37,8326639499581 | 49,0660677694388 | |||||
| 29,3339111535563 | 44,061347061597 | |||||
| 25,945544179828 | 40,8450726700601 | |||||
| 23,4472995238777 | 39,6156341666274 | |||||
| 36,1330815505422 | 49,427532888675 | |||||
| 30,2783586200406 | 45,3305954491812 | |||||
| 28,4849558227767 | 43,0882903027858 | |||||
| 25,4946422141971 | 39,6301462386908 | |||||
| 39,3005222465473 | 50,509555744214 | |||||
| 31,616762561846 | 45,6892192575785 | |||||
| 26,357535056778 | 41,6042690300731 | |||||
| 23,3006176833199 | 38,8873160464746 | |||||
| 38,6761679930968 | 50,952926485391 | |||||
| 32,0234700797161 | 45,2806968991624 | |||||
| 27,4444695906714 | 41,9154328758198 | |||||
| 23,1447042234213 | 40,2872834981624 | |||||
| 36,9573307126995 | 50,2830605818109 | |||||
| 30,6409299220892 | 45,7905348233713 | |||||
| 25,1619589999512 | 42,6305823689336 | |||||
| 23,0323473291704 | 40,0269977520094 | |||||
| 36,6924054384558 | 42,1129305385315 | |||||
| 36,3758803477696 | 42,9674522154126 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 53 | |
| 49,6 | |
| 51,1 | |
| 51,1 | |
| 50 | |
| 50 | |
| 50,3 | |
| 52 | |
| 52 | |
| 57 | |
| 56 | |
| 59,8 | |
| 59,1 | |
| 58,9 | |
| 57 | |
| 57 | |
| 59,5 | |
| 62,5 | |
| 66,6 | |
| 71 | |
| 73,2 | |
| 78,5 | |
| 78,5 | |
| 80 | |
| 81 | |
| 88,8 | |
| 83,5 | |
| 84,7 | |
| 84 | |
| 90 | |
| 97,4 | |
| 92 | |
| 89,9 | |
| 90,8 | |
| 87 | |
| 89,9 | |
| 89,3 | |
| 93,5 | |
| 95,5 | |
| 90,9 | |
| 96 | |
| 95 | |
| 96 | |
| 92 | |
| 89,6 | |
| 87,5 | |
| 93 | |
| 81,5 | |
| 88 | |
| 95 |
| Yt | Xt | dane kwartalne | ||||
| 20,1127432256159 | 25,4327 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 20,684535774468 | 24,1043 | Yt | ||||
| 26,8776559015158 | 15,6247 | Xt | 0 | + | 2 | |
| 20,9937015411991 | 25,7428290413533 | |||||
| 21,9107551616107 | 25,4134602107025 | |||||
| 24,0340909764375 | 22,1911901999061 | |||||
| 29,833763790308 | 13,1606901302175 | |||||
| 22,3175596971194 | 24,0207330284325 | |||||
| 23,5741947621081 | 25,7876517282962 | |||||
| 25,0091875525615 | 23,0042830396848 | |||||
| 33,0139235606183 | 13,716866308029 | |||||
| 27,6501690333759 | 22,1946313571301 | |||||
| 27,1686563424295 | 22,1683304941821 | |||||
| 30,4406889833579 | 18,1123605692742 | |||||
| 37,0689633410425 | 10,2096794660749 | |||||
| 29,1358234337453 | 22,807562633373 | |||||
| 30,1417400082239 | 25,4524886939294 | |||||
| 29,9050445876062 | 24,4852755402514 | |||||
| 32,5440754981415 | 18,6072010398657 | |||||
| 25,570279783942 | 29,7035736775589 | |||||
| 25,8670810870127 | 29,7982369482151 | |||||
| 31,6951989003955 | 22,1635628073411 | |||||
| 41,3546739390274 | 7,60858723835225 | |||||
| 35,7570263657822 | 14,8219330547566 | |||||
| 35,5797705917128 | 15,2895643730935 | |||||
| 36,8605516836467 | 13,7509632476687 | |||||
| 41,9319748875703 | 9,00383326048572 | |||||
| 30,9202843132245 | 23,9009662938754 | |||||
| 30,0716352082217 | 28,5761961357634 | |||||
| 28,7521098453657 | 27,3692441527337 | |||||
| 35,8871466410647 | 18,2005141221868 | |||||
| 28,5487025679899 | 27,4085028580385 | |||||
| 28,3259688940063 | 25,1958418628936 | |||||
| 33,9601646527457 | 20,524394408395 | |||||
| 44,0694871532561 | 8,48697337682783 | |||||
| 35,8741162571666 | 19,614202435369 | |||||
| 35,2816270731357 | 20,8284478574454 | |||||
| 39,1839343352869 | 17,5486343800805 | |||||
| 46,7164965254407 | 6,87441193642793 | |||||
| 39,2790977073096 | 16,8055881562123 | |||||
| 37,7904573766526 | 19,3680703071545 | |||||
| 38,6783764085632 | 18,6492831508561 | |||||
| 43,0195493944622 | 14,1440897649308 | |||||
| 33,5609564092565 | 27,9631887881187 | |||||
| 32,2595471018711 | 29,9551212725523 | |||||
| 34,5372755061167 | 26,0660241267768 | |||||
| 42,7647540561202 | 14,0771294575458 | |||||
| 35,6265114808997 | 23,7255854179742 | |||||
| 38,6913107815599 | 22,5551201569675 | |||||
| 42,2299506615262 | 18,3019653749712 | |||||
| 50,968512975726 | 7,46873645868318 | |||||
| 45,6308333002696 | 16,824009496419 | |||||
| 43,6889712964152 | 19,2212523814556 | |||||
| 47,1278168899176 | 16,9113952635518 | |||||
| 52,4382118072217 | 7,75820527837286 | |||||
| 44,7789079557179 | 18,9423727082 | |||||
| 41,7427600882115 | 23,1369115825844 | |||||
| 41,4431925708859 | 23,608323094755 | |||||
| 45,7899755469526 | 16,5631965272821 | |||||
| 38,6278126203748 | 28,7166236583718 | |||||
| 38,7892597416758 | 28,7312209788411 | |||||
| 41,0694755072774 | 23,072292273611 | |||||
| 52,5162779393891 | 9,10296875682071 | |||||
| 48,4139183731503 | 15,7141869646632 | |||||
| 47,5983953902644 | 15,8714272623225 | |||||
| 48,8777353856598 | 13,9929153515191 | |||||
| 53,845677273768 | 8,6723800263403 | |||||
| 43,8743613465002 | 22,8856842257773 | |||||
| 41,3733012969048 | 25,3930527375374 | |||||
| 43,0889587454245 | 23,0060685768603 | |||||
| 52,2681511430237 | 12,9275622591928 | |||||
| 46,5889247802472 | 22,7618378955342 | |||||
| 42,7113736952779 | 24,3695345995812 | |||||
| 44,9765026631449 | 21,7019012533492 | |||||
| 51,4068408723277 | 12,2260608657356 | |||||
| 46,1191480548259 | 22,1165862571627 | |||||
| 44,7739326417791 | 23,0212832322982 | |||||
| 48,0130037549099 | 20,5348255402308 | |||||
| 55,5216909744394 | 10,7759659553009 | |||||
| 48,3087952206135 | 23,2323025422737 | |||||
| 49,2080046046366 | 24,5091147078671 | |||||
| 50,6569415589217 | 21,865611244541 | |||||
| 58,1291762731406 | 11,8844747541853 | |||||
| 49,7233393801225 | 22,7551094866095 | |||||
| 48,4975476846585 | 24,2848478998085 | |||||
| 48,8054581789456 | 23,415858101745 | |||||
| 57,5297042980419 | 13,0564098529644 | |||||
| 51,7636354053612 | 23,8162834731725 | |||||
| 48,8416044030217 | 25,6088846894081 | |||||
| 49,1023643158868 | 24,6671603771976 | |||||
| 55,2603213378133 | 15,386060383049 | |||||
| 47,528507932783 | 25,1045522734005 | |||||
| 48,6658256620266 | 25,7922292926967 | |||||
| 51,654341441262 | 21,9474698222543 | |||||
| 60,2570674752622 | 11,3550453521798 | |||||
| 52,7169346488304 | 22,5385497234589 | |||||
| 51,4747665002755 | 25,3675387405723 | |||||
| 53,6892534694114 | 23,1769672338028 | |||||
| 60,0874574778528 | 15,2997627075693 | |||||
| 50,540239086024 | 26,2299498216884 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | -0,276 | y2t + | 0,363 | y1t-1 + | -0,465 | y2t-1 + | 0,281 | x1t + | -0,468 | x2t + | 0,097 | x3t |
| y2t | = | -0,423 | y1t + | -0,159 | y1t-1 + | 0,118 | y2t-1 + | -0,182 | x1t + | -0,374 | x2t + | -0,102 | x3t |
| Yt | Xt | dane kwartalne | ||||
| 18,4812 | 39,6926 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,0478 | 41,8883 | Yt | ||||
| 16,4355 | 40,8452 | Xt | 2 | - | 2 | |
| 15,6454772699588 | 42,0374256078394 | |||||
| 15,1003824100089 | 44,1383319030513 | |||||
| 16,6673985004739 | 43,8918476396526 | |||||
| 16,0978293143726 | 46,1701726752508 | |||||
| 15,3561425841282 | 46,9836995421698 | |||||
| 15,0505473941663 | 49,5768452818178 | |||||
| 14,4656809301967 | 49,5281982042931 | |||||
| 14,8422930889878 | 48,9542102253537 | |||||
| 12,5317691278527 | 49,8638444492828 | |||||
| 13,7082002646623 | 51,4208957346424 | |||||
| 12,4988707728219 | 53,1903894040004 | |||||
| 14,1636820532073 | 54,2403766146717 | |||||
| 13,3708561855229 | 54,9888727650686 | |||||
| 12,4799950710895 | 56,4803737830931 | |||||
| 13,1518903943399 | 57,6061749602235 | |||||
| 15,1110285847215 | 58,2148952274708 | |||||
| 12,047751931502 | 60,2108230989436 | |||||
| 12,8702144862491 | 59,0439501940833 | |||||
| 10,1666951804362 | 59,5142154578446 | |||||
| 10,0569950838195 | 61,2422961443212 | |||||
| 10,5802009609985 | 62,3035753661596 | |||||
| 10,8396681530587 | 63,3434709175996 | |||||
| 10,032301783193 | 64,3072732938079 | |||||
| 11,2943789683332 | 65,4877151340032 | |||||
| 9,93330798496175 | 66,0322313948397 | |||||
| 10,4159661020249 | 66,0777495311352 | |||||
| 9,77863032450034 | 68,0909535334862 | |||||
| 9,83973710166825 | 70,0364315071674 | |||||
| 9,71694205267647 | 70,7710818961697 | |||||
| 8,51591271150063 | 72,2736464570344 | |||||
| 10,3802699983704 | 72,4054422035798 | |||||
| 8,28918678677024 | 72,3592475900251 | |||||
| 9,41196124692289 | 76,579410595294 | |||||
| 7,02890935417066 | 77,6580147201126 | |||||
| 6,2341683773859 | 77,0275237689862 | |||||
| 4,65101823416112 | 78,840506563572 | |||||
| 4,85637871980363 | 80,4572978716315 | |||||
| 6,21096188173577 | 81,7752178359382 | |||||
| 5,9622326249922 | 82,161927560049 | |||||
| 7,54588612015317 | 85,503127456832 | |||||
| 6,1112601016642 | 85,161565470723 | |||||
| 5,5434316880756 | 85,7872006969228 | |||||
| 5,74170660347362 | 85,9827671846245 | |||||
| 5,04714468320482 | 87,6885667344653 | |||||
| 7,2466439043594 | 88,0414732568612 | |||||
| 4,11967156581168 | 91,5718759558514 | |||||
| 4,40241702173634 | 92,3762557309683 | |||||
| 3,52252936604562 | 91,362627101217 | |||||
| 1,76171709027635 | 95,3486996942931 | |||||
| 2,76247446218357 | 98,2158544574738 | |||||
| 0,673721766531013 | 98,7339018441309 | |||||
| -0,033050025939165 | 99,8056898461576 | |||||
| 0,293284100272192 | 100,865595569637 | |||||
| 2,29749503087833 | 103,277300258623 | |||||
| 2,36187374652954 | 102,946000989522 | |||||
| 1,18472751412921 | 105,702140344084 | |||||
| 1,539361065023 | 107,045955939729 | |||||
| 0,677572846654254 | 106,383954307075 | |||||
| -0,003793504954544 | 108,253990534884 | |||||
| -2,22665014355733 | 111,456705352539 | |||||
| -2,04698062532987 | 112,232084034039 | |||||
| -0,821079928979628 | 113,411792543108 | |||||
| -1,29661692954954 | 113,330000210435 | |||||
| -0,766079219233347 | 115,943441575553 | |||||
| -3,21507167506722 | 119,471176588134 | |||||
| -4,10914217549373 | 118,549182320143 | |||||
| -4,10699627490945 | 121,78513761043 | |||||
| -3,7665675707552 | 120,898618580144 | |||||
| -3,59069877167626 | 123,277019909971 | |||||
| -2,79438239386189 | 125,84248424796 | |||||
| -4,70277176294647 | 129,82138971719 | |||||
| -5,19649965030099 | 130,271859037284 | |||||
| -5,92017647708903 | 131,202665671476 | |||||
| -5,18221904859858 | 131,348894461134 | |||||
| -5,83019767915089 | 134,602924650158 | |||||
| -6,97605540399235 | 134,599090967837 | |||||
| -4,53182668258744 | 134,524651457103 | |||||
| -7,81557521496478 | 138,605342389274 | |||||
| -6,92416099855974 | 138,128906664289 | |||||
| -8,71945385606746 | 142,063194187861 | |||||
| -7,86766714256964 | 143,434896342287 | |||||
| -7,9934052057562 | 144,077419699342 | |||||
| -7,65797830176528 | 148,09868861128 | |||||
| -11,2132761387456 | 148,991091504643 | |||||
| -8,28816913882145 | 146,860298879601 | |||||
| -8,67753216524997 | 150,077001250912 | |||||
| -8,4773049333239 | 153,250440724444 | |||||
| -10,6767018982748 | 153,874776039595 | |||||
| -10,8715543158433 | 154,403822270949 | |||||
| -10,7611051639616 | 157,964473700461 | |||||
| -12,3739027293277 | 161,077325025994 | |||||
| -12,8061726697034 | 161,166635270306 | |||||
| -11,7075295663217 | 162,694189102923 | |||||
| -12,0241037103104 | 165,192648587108 | |||||
| -13,8678701379487 | 166,569821614259 | |||||
| -12,670079139953 | 166,875698928282 | |||||
| -14,1474823591257 | 168,887115248461 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Wintersa |
| b) | policzyć prognozy oraz błędy prognoz |
| yt | |
| 332596 | |
| 330998 | |
| 366647 | |
| 363664 | |
| 504367 | |
| 558975 | |
| 554609 | |
| 513601 | |
| 470333 | |
| 425586 | |
| 331736 | |
| 316112 | |
| 346839 | |
| 328057 | |
| 376914 | |
| 381307 | |
| 470549 | |
| 589625 | |
| 573379 | |
| 481027 | |
| 444179 | |
| 419558 | |
| 325963 | |
| 303565 | |
| 336469 | |
| 319614 | |
| 369843 | |
| 391803 | |
| 475097 | |
| 595903 | |
| 591491 | |
| 559410 | |
| 523380 | |
| 463932 | |
| 351063 | |
| 331086 | |
| 353070 | |
| 339084 | |
| 381429 | |
| 393236 | |
| 522463 | |
| 611667 | |
| 597763 | |
| 525054 | |
| 507200 | |
| 470763 | |
| 375066 | |
| 379495 | |
| 410678 | |
| 407783 | |
| 457506 | |
| 473943 | |
| 637559 | |
| 726153 | |
| 682582 | |
| 654554 | |
| 638730 | |
| 599457 | |
| 469232 | |
| 441060 | |
| 475435 | |
| 449198 | |
| 520786 | |
| 518934 | |
| 697969 | |
| 804968 | |
| 775588 | |
| 742621 | |
| 709088 | |
| 637739 | |
| 513214 | |
| 512842 | |
| 563484 | |
| 526395 | |
| 595654 | |
| 593429 | |
| 750967 | |
| 909751 | |
| 887626 | |
| 806736 | |
| 758042 | |
| 659707 | |
| 514318 | |
| 485064 | |
| 513733 | |
| 480235 | |
| 554126 | |
| 579897 | |
| 781771 | |
| 905767 | |
| 878118 | |
| 826922 | |
| 783158 | |
| 701655 | |
| 539899 | |
| 547867 |
| Yt | Xt | dane kwartalne | ||||
| 23,8004 | 30,3890 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 22,7878 | 28,6143 | Yt | - | 2 | ||
| 23,0477 | 28,6890 | Xt | 1 | |||
| 23,9089772406916 | 28,2567049523106 | |||||
| 24,1808835666858 | 28,3418819809242 | |||||
| 24,0160602549358 | 29,8349527923697 | |||||
| 23,0294497149823 | 29,9488811169479 | |||||
| 22,8932556440185 | 29,4512524467792 | |||||
| 25,8422124527178 | 29,9236009787117 | |||||
| 24,5162873512346 | 29,3241403914847 | |||||
| 25,0644630670345 | 29,5285561565939 | |||||
| 24,0046885790399 | 27,4909224626375 | |||||
| 23,6827926697668 | 29,134468985055 | |||||
| 23,4768046813143 | 28,455987594022 | |||||
| 25,5798355077843 | 30,4357950376088 | |||||
| 25,8401847367207 | 29,8675180150435 | |||||
| 27,7043850709142 | 29,4241072060174 | |||||
| 26,0849094563966 | 30,433742882407 | |||||
| 24,5418681437063 | 32,5754971529628 | |||||
| 24,3765478096471 | 30,1109988611851 | |||||
| 25,6478880915968 | 30,583399544474 | |||||
| 24,7038595548584 | 28,0209598177896 | |||||
| 23,8085752907318 | 28,4296839271158 | |||||
| 23,310389555221 | 29,2712735708463 | |||||
| 23,910411100916 | 29,8427094283385 | |||||
| 24,0928442481017 | 29,3244837713354 | |||||
| 26,5432310194601 | 30,9406935085342 | |||||
| 24,7354501255731 | 29,7429774034137 | |||||
| 26,629060913058 | 30,2392909613655 | |||||
| 23,8465774813008 | 30,2059163845462 | |||||
| 24,4344182917105 | 30,8506665538185 | |||||
| 23,960990031456 | 30,9482666215274 | |||||
| 22,0085061802113 | 30,198006648611 | |||||
| 25,8427457414674 | 32,1019026594444 | |||||
| 26,6428268809897 | 29,9969610637777 | |||||
| 26,2243270637824 | 32,3857844255111 | |||||
| 24,2842704058854 | 30,3263137702044 | |||||
| 25,1572390591244 | 29,3424255080818 | |||||
| 24,4392641979232 | 28,3031702032327 | |||||
| 23,6578156972749 | 28,9935680812931 | |||||
| 24,5839757156807 | 30,7435272325172 | |||||
| 24,962401999226 | 30,6108108930069 | |||||
| 27,290646825136 | 33,1968243572028 | |||||
| 26,1997832288911 | 31,6597297428811 | |||||
| 25,3905847333411 | 31,2795918971524 | |||||
| 24,7064872645778 | 31,536536758861 | |||||
| 24,4510301589164 | 31,3537147035444 | |||||
| 25,4064636787368 | 33,6590858814178 | |||||
| 26,7476257031542 | 31,5912343525671 | |||||
| 27,1559749125404 | 32,1152937410268 | |||||
| 26,5969202111576 | 30,9313174964107 | |||||
| 26,5992958181502 | 30,3663269985643 | |||||
| 26,4608031202612 | 32,2272307994257 | |||||
| 26,7908003244989 | 30,2938923197703 | |||||
| 25,1049992300964 | 29,9086569279081 | |||||
| 25,1389605192687 | 30,5529627711633 | |||||
| 26,4979808912335 | 33,2806851084653 | |||||
| 26,5749124500873 | 33,2456740433861 | |||||
| 25,7523310217741 | 32,8953696173544 | |||||
| 27,4437744015011 | 33,6531478469418 | |||||
| 26,9040859444744 | 32,5927591387767 | |||||
| 24,5541948718893 | 32,4724036555107 | |||||
| 25,5361653406433 | 31,2103614622043 | |||||
| 26,5034166839713 | 31,6226445848817 | |||||
| 26,0266807298792 | 33,2024578339527 | |||||
| 25,2831891557828 | 32,7023831335811 | |||||
| 27,2522398773415 | 34,0169532534324 | |||||
| 26,3783229993014 | 32,626281301373 | |||||
| 24,4896684593945 | 31,4556125205492 | |||||
| 24,8549488990853 | 32,4285450082197 | |||||
| 27,2254885393957 | 32,5030180032879 | |||||
| 28,5009904510408 | 33,3924072013151 | |||||
| 25,3138810041291 | 34,9583628805261 | |||||
| 24,9565363029233 | 34,2436451522104 | |||||
| 25,3970760246913 | 33,8850580608842 | |||||
| 27,172370991256 | 33,4406232243537 | |||||
| 26,4291902361356 | 34,2224492897415 | |||||
| 27,333904839857 | 34,5506797158966 | |||||
| 27,0094287567542 | 33,4036718863586 | |||||
| 29,0650112894866 | 35,8255687545435 | |||||
| 29,0312493629436 | 33,7660275018174 | |||||
| 27,9035052327165 | 34,514511000727 | |||||
| 27,2227063827114 | 33,8995044002908 | |||||
| 26,8921030516353 | 35,1628017601163 | |||||
| 26,868975183042 | 35,2298207040465 | |||||
| 27,6183359048455 | 36,7716282816186 | |||||
| 27,5736670890362 | 33,4840513126474 | |||||
| 30,1676244496749 | 35,769920525059 | |||||
| 27,7079237687707 | 36,3455682100236 | |||||
| 27,1535842177406 | 37,4978272840094 | |||||
| 26,2566588455421 | 35,4857309136038 | |||||
| 25,8505917043701 | 35,4495923654415 | |||||
| 28,3920782172909 | 36,6282369461766 | |||||
| 28,2191886048418 | 35,9492947784706 | |||||
| 28,4040916402366 | 35,5438179113883 | |||||
| 28,6930925598669 | 37,1007271645553 | |||||
| 28,994855116343 | 37,5336908658221 | |||||
| 28,5434243216036 | 36,1030763463289 | |||||
| 29,6119554384558 | 37,3926305385315 | |||||
| 26,7026803477696 | 36,5186522154126 |
| Zadanie |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich dwóch obserwacji) |
| dokonać wyrównania wykładniczego |
| oraz wyrównać szereg za pomocą sredniej 3-wyrazowj. |
| Obliczyć prognozy. Która metoda dała lepsze wyniki? |
| Pt |
| 127,5 |
| 131 |
| 136 |
| 142 |
| 142,5 |
| 141,5 |
| 140 |
| 143,5 |
| 144 |
| 149,5 |
| 155 |
| 155 |
| 149,5 |
| 144 |
| 150 |
| 150 |
| 148 |
| 150 |
| 157,5 |
| 160 |
| 159 |
| 160 |
| 159,5 |
| 169 |
| 174 |
| 174 |
| 199 |
| 195 |
| 187 |
| 187 |
| 184 |
| 195 |
| 190 |
| 177,5 |
| 177 |
| 172 |
| 177 |
| 185 |
| 180 |
| 190 |
| 207 |
| 207 |
| 205,5 |
| 195 |
| 183 |
| 176 |
| 184 |
| 161 |
| 163 |
| 176,5 |
| Yt | Xt | dane kwartalne | ||||
| 27,8175 | 36,9152 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 27,3970 | 35,6148 | Yt | 0 | |||
| 29,6933 | 37,1923 | Xt | - | 1 | ||
| 28,0384406094238 | 37,1393263586858 | |||||
| 27,5210118588343 | 36,0525305434743 | |||||
| 29,8375961732191 | 36,8193122173897 | |||||
| 29,602708499611 | 38,1477248869559 | |||||
| 27,6470359861004 | 36,9991899547824 | |||||
| 30,3704046784712 | 38,5870759819129 | |||||
| 28,2260162375272 | 36,1252303927652 | |||||
| 29,2333865928709 | 35,1696921571061 | |||||
| 28,7753883762368 | 37,8576768628424 | |||||
| 27,6730981906809 | 37,356770745137 | |||||
| 28,0063455746389 | 37,4433082980548 | |||||
| 28,208493526983 | 36,5511233192219 | |||||
| 29,5904831698469 | 38,4084493276888 | |||||
| 31,5538895583274 | 37,0306797310755 | |||||
| 29,8932332408092 | 37,3738718924302 | |||||
| 28,7505081179462 | 38,9018487569721 | |||||
| 27,0230724327463 | 38,9501395027888 | |||||
| 27,3813041193956 | 38,2119558011155 | |||||
| 27,3038534652365 | 37,6995823204462 | |||||
| 28,0957997509446 | 37,9063329281785 | |||||
| 30,0750145375593 | 38,3212331712714 | |||||
| 30,1377556241595 | 38,6830932685086 | |||||
| 28,3162037630772 | 35,2424373074034 | |||||
| 29,4804673191969 | 35,9588749229614 | |||||
| 29,3580943806377 | 38,0277499691845 | |||||
| 30,4096007345448 | 39,9499999876738 | |||||
| 29,9539345490751 | 39,3759999950695 | |||||
| 29,7382370525717 | 37,6882999980278 | |||||
| 30,5492731609224 | 39,1338199992111 | |||||
| 29,8495194644333 | 39,9795279996844 | |||||
| 31,9564243838374 | 39,7059111998738 | |||||
| 31,7852899925477 | 40,7339644799495 | |||||
| 28,2119061371062 | 40,2715857919798 | |||||
| 27,1908814531822 | 39,5864343167919 | |||||
| 27,9091350384166 | 37,5964737267168 | |||||
| 29,5951445444366 | 38,6363894906867 | |||||
| 29,3479833451665 | 38,6573557962747 | |||||
| 30,6312889430415 | 38,9028423185099 | |||||
| 29,6740607214865 | 39,2214369274039 | |||||
| 29,9015481792371 | 39,3708747709616 | |||||
| 30,2485276737351 | 40,2539499083846 | |||||
| 28,9290331033214 | 39,3931799633539 | |||||
| 26,4881417376302 | 37,7497719853415 | |||||
| 27,8891993330547 | 38,3692087941366 | |||||
| 28,8020125033327 | 39,5007835176546 | |||||
| 27,1156385949877 | 38,0304134070619 | |||||
| 29,2329124037891 | 38,6741653628247 | |||||
| 29,6614183663163 | 39,4212661451299 | |||||
| 29,6864469591886 | 39,973406458052 | |||||
| 28,9983675685663 | 40,3424625832208 | |||||
| 29,0558875360733 | 39,9074850332883 | |||||
| 28,1851286332855 | 41,6595940133153 | |||||
| 27,8474911101482 | 40,1809376053261 | |||||
| 28,6231991868195 | 40,5291750421305 | |||||
| 29,7497341490577 | 40,7050700168522 | |||||
| 31,02613007396 | 41,5718280067409 | |||||
| 29,9866138944535 | 40,8867312026963 | |||||
| 30,1259555659151 | 41,8607924810785 | |||||
| 31,092363670972 | 40,9483169924314 | |||||
| 32,7496981882517 | 41,1533267969726 | |||||
| 31,3973712018503 | 41,237230718789 | |||||
| 31,4684136280561 | 42,3806922875156 | |||||
| 30,6552454469155 | 41,3366769150063 | |||||
| 29,946368632418 | 42,8508707660025 | |||||
| 31,1559686810851 | 42,597148306401 | |||||
| 32,0577469503975 | 42,1550593225604 | |||||
| 32,3154521507053 | 41,6449237290242 | |||||
| 33,3166647021663 | 41,3314694916097 | |||||
| 32,4964617906447 | 41,8617877966439 | |||||
| 32,2497625185817 | 43,1889151186576 | |||||
| 31,6163651356612 | 43,426366047463 | |||||
| 32,2669227776815 | 41,3660464189852 | |||||
| 32,3285044343126 | 43,3492185675941 | |||||
| 31,4698714183199 | 42,5845874270376 | |||||
| 32,3237877926534 | 41,7839349708151 | |||||
| 30,6507738363456 | 40,889073988326 | |||||
| 29,3677371265827 | 41,3167295953304 | |||||
| 30,4451610308701 | 41,6752918381322 | |||||
| 32,3258042248532 | 43,4495167352529 | |||||
| 29,3604217421227 | 41,9967066941011 | |||||
| 30,3866617791883 | 42,4810826776405 | |||||
| 33,0622562371905 | 43,6252330710562 | |||||
| 33,985380332932 | 42,6855932284225 | |||||
| 32,3173685945462 | 42,441337291369 | |||||
| 31,7953923170884 | 42,9086349165476 | |||||
| 30,6515044280583 | 41,871353966619 | |||||
| 31,9139120580538 | 42,3364415866476 | |||||
| 32,1968357162699 | 43,8036766346591 | |||||
| 32,311726646983 | 42,8010706538636 | |||||
| 31,7778105711162 | 42,1990282615454 | |||||
| 32,0237964764655 | 43,9880113046182 | |||||
| 30,2818087408988 | 42,8754045218473 | |||||
| 30,8645968971101 | 43,0797618087389 | |||||
| 29,7580784141256 | 43,2967047234956 | |||||
| 31,7949391730658 | 43,5467818893982 | |||||
| 32,3369126763497 | 43,5437127557593 |
| Zadanie | |||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||
| y1t | = | 0,142 | y2t + | 0,396 | y1t-1 + | -0,19 | y2t-1 + | 0,194 | x1t + | -0,326 | x2t |
| y2t | = | 0,065 | y1t + | -0,423 | y1t-1 + | 0,282 | y2t-1 + | -0,155 | x1t + | 0,12 | x2t |
| Yt | Xt | dane miesięczne | ||||
| 33,1243 | 43,3477 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 32,8548 | 45,3088 | Yt | 0 | 2 | ||
| 32,8502 | 46,0486 | Xt | - | |||
| 33,2406280181266 | 45,475041858619 | |||||
| 32,4457942560273 | 46,4586167434476 | |||||
| 33,5013341641961 | 47,380446697379 | |||||
| 33,9636989819381 | 46,1923786789516 | |||||
| 32,7062473123695 | 45,7650514715806 | |||||
| 33,401918189867 | 46,8738205886323 | |||||
| 32,8682015925281 | 44,8250282354529 | |||||
| 35,0333970158262 | 46,6155112941812 | |||||
| 33,1027167007635 | 44,4090045176725 | |||||
| 31,0302157138775 | 43,157201807069 | |||||
| 32,8121834340071 | 44,3974807228276 | |||||
| 33,1200832377593 | 45,284892289131 | |||||
| 33,3892140826451 | 45,1950569156524 | |||||
| 34,7649130675818 | 45,985922766261 | |||||
| 32,7062547080322 | 47,0603691065044 | |||||
| 32,0309233933555 | 47,4871476426018 | |||||
| 31,0343832681137 | 46,5148590570407 | |||||
| 32,2194938095884 | 45,4722436228163 | |||||
| 32,4902486017754 | 44,4676974491265 | |||||
| 33,6406778289773 | 44,3701789796506 | |||||
| 32,7595600023425 | 45,0319715918602 | |||||
| 31,9132549198326 | 46,6130886367441 | |||||
| 32,7157007661554 | 47,8178354546976 | |||||
| 32,8248954299046 | 47,5818341818791 | |||||
| 34,5138710942164 | 45,1032336727516 | |||||
| 32,4552303617811 | 45,2527934691007 | |||||
| 31,3622992300833 | 45,1895173876403 | |||||
| 32,3032736574904 | 46,4905069550561 | |||||
| 32,9940493201134 | 46,3114027820224 | |||||
| 33,6328984669669 | 46,739061112809 | |||||
| 31,0918417991123 | 44,9589244451236 | |||||
| 31,3489143041313 | 46,5942697780494 | |||||
| 31,379729790198 | 46,0697079112198 | |||||
| 32,810395675006 | 46,5907831644879 | |||||
| 33,7191959289022 | 46,6995132657952 | |||||
| 31,9843210733327 | 47,1370053063181 | |||||
| 30,9806784825491 | 47,1414021225272 | |||||
| 33,1301736090961 | 47,1362608490109 | |||||
| 33,4982805357119 | 47,2135043396044 | |||||
| 31,7193020954985 | 46,4801017358417 | |||||
| 33,4109874511843 | 46,8446406943367 | |||||
| 33,426486322602 | 48,3516562777347 | |||||
| 34,2113602162095 | 47,3888625110939 | |||||
| 34,5182395274297 | 48,7345450044375 | |||||
| 33,6557638252942 | 49,450318001775 | |||||
| 31,6673759049951 | 48,25512720071 | |||||
| 33,69680014514 | 48,998550880284 | |||||
| 35,4122288371638 | 49,9336203521136 | |||||
| 35,5591759894768 | 50,6558481408454 | |||||
| 34,959169989364 | 49,7371392563382 | |||||
| 35,1456524561489 | 50,0794557025353 | |||||
| 34,8400733345892 | 49,2533822810141 | |||||
| 33,2565401717795 | 49,0954529124056 | |||||
| 32,5023827820448 | 48,3635811649623 | |||||
| 35,4695682181013 | 50,4606324659849 | |||||
| 37,3945248258823 | 49,795552986394 | |||||
| 37,3144091680888 | 49,4780211945576 | |||||
| 34,9886290245109 | 49,343708477823 | |||||
| 32,8169595171213 | 47,2615833911292 | |||||
| 34,0665681533244 | 46,1532333564517 | |||||
| 32,9269220623726 | 47,9901933425807 | |||||
| 34,3884659215277 | 48,7290773370323 | |||||
| 35,3957314765876 | 50,2068309348129 | |||||
| 33,8877960156497 | 50,7244323739252 | |||||
| 35,9952315863742 | 52,2006729495701 | |||||
| 33,9027581971025 | 50,268169179828 | |||||
| 32,8089521060831 | 50,1739676719312 | |||||
| 32,9043755872884 | 49,5023870687725 | |||||
| 33,4672779591704 | 49,966354827509 | |||||
| 32,7027166223391 | 48,4880419310036 | |||||
| 35,3340260509946 | 50,0046167724014 | |||||
| 34,977623489826 | 47,6509467089606 | |||||
| 34,9326491100268 | 50,1783786835842 | |||||
| 33,8709605802305 | 50,8617514734337 | |||||
| 33,8726047859731 | 49,5678005893735 | |||||
| 33,4200869104638 | 47,8479202357494 | |||||
| 36,3671860960585 | 48,6554680942998 | |||||
| 34,7393816055375 | 49,0897872377199 | |||||
| 35,1410158262102 | 50,316414895088 | |||||
| 35,5553407723474 | 50,9225659580352 | |||||
| 36,0886995746721 | 50,0102263832141 | |||||
| 34,1267711301764 | 49,5209905532856 | |||||
| 34,9419601225044 | 50,1013962213143 | |||||
| 36,8555774941264 | 50,8266584885257 | |||||
| 35,4119272190827 | 50,8409633954103 | |||||
| 35,2878409648118 | 50,3155853581641 | |||||
| 35,3077575580844 | 51,3015341432657 | |||||
| 35,92633758616 | 51,8781136573063 | |||||
| 37,0008159642792 | 52,6857454629225 | |||||
| 33,9325364817414 | 52,202498185169 | |||||
| 33,7283603617669 | 51,4449992740676 | |||||
| 35,984644000433 | 51,998999709627 | |||||
| 35,4409137973152 | 51,8415998838508 | |||||
| 36,1769336607792 | 52,6214399535403 | |||||
| 35,1779106760957 | 51,8436759814161 | |||||
| 34,2505074337743 | 51,3680703925665 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | 0,166 | y2t + | -0,232 | y1t-1 + | 0,234 | y2t-1 + | 0,493 | y3t-1 + | -0,354 | x1t + | -0,085 | x2t |
| y2t | = | -0,072 | y3t + | 0,243 | y1t-1 + | -0,209 | y2t-1 + | 0,461 | y3t-1 + | -0,359 | x1t + | -0,007 | x2t |
| y3t | = | 0,048 | y1t + | -0,375 | y1t-1 + | 0,311 | y2t-1 + | 0,189 | y3t-1 + | 0,427 | x1t + | 0,435 | x2t |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | ||||
| 12,3805 | 25,9273 | Xt | 2 | + | 3 | |
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | |||
| Wiedząc, że dla poniższych danych (z pominięciem ostatnich dwóch obserwacji) pominięciemzachodzi zależność | |||
| Y1t=f1(stała, Y2t, Y1,t-1, Xt-1) | |||
| Y2t=f2(stała, Y1t, Xt, Xt-1, t) | |||
| Wyznaczyć prognozę na dwa okresy w przód oraz błędy prognoz | |||
| t | Y1t | Y2t | Xt |
| 1962 | 176 | 301 | 52 |
| 1963 | 185 | 317 | 52 |
| 1964 | 188 | 342 | 53 |
| 1965 | 198 | 356 | 53 |
| 1966 | 199 | 373 | 56 |
| 1967 | 201 | 381 | 59 |
| 1968 | 205 | 407 | 62 |
| 1969 | 211 | 432 | 66 |
| 1970 | 216 | 436 | 70 |
| 1971 | 214 | 438 | 70 |
| 1972 | 215 | 440 | 72 |
| 1973 | 220 | 444 | 73 |
| 1974 | 223 | 460 | 71 |
| 1975 | 224 | 480 | 65 |
| 1976 | 223 | 475 | 63 |
| 1977 | 224 | 483 | 57 |
| 1978 | 226 | 510 | 59 |
| 1979 | 225 | 501 | 60 |
| 1980 | 224 | 514 | 61 |
| 1981 | 226 | 520 | 61 |
| 1982 | 227 | 524 | 62 |
| 1983 | 230 | 538 | 65 |
| 1984 | 232 | 543 | 64 |
| 1985 | 235 | 560 | 63 |
| Yt | Xt | dane kwartalne | ||||
| 48,1183107138122 | 64,1442 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 44,6353997167258 | 65,9714 | Yt | 1 | |||
| 39,0506105076807 | 67,1621 | Xt | 3 | - | ||
| 33,4033278345713 | 68,190702584866 | |||||
| 51,9950409479241 | 69,6209053537098 | |||||
| 48,9929799569888 | 72,7457716429085 | |||||
| 43,4407589077525 | 76,0440236799703 | |||||
| 37,2680251252945 | 78,1779031828218 | |||||
| 58,2534578266532 | 80,3016421194227 | |||||
| 53,9494482767622 | 82,0676597865827 | |||||
| 49,7315457144966 | 84,0730730455222 | |||||
| 42,6088408999317 | 84,1918726081281 | |||||
| 59,9825558408614 | 85,7002070858551 | |||||
| 56,9810533988051 | 87,2920544996764 | |||||
| 53,0352352822315 | 90,5910444154961 | |||||
| 47,6299567411805 | 93,3200004078775 | |||||
| 68,350169487491 | 94,8349824377403 | |||||
| 63,67413466217 | 97,1279910557192 | |||||
| 57,8746208435369 | 102,003502552763 | |||||
| 52,7447622106246 | 104,507854854094 | |||||
| 71,3282305947596 | 106,221826405942 | |||||
| 67,274094326561 | 105,707671261333 | |||||
| 60,0636818820922 | 105,79930506829 | |||||
| 53,1345066887794 | 107,733184029612 | |||||
| 72,2390923307317 | 110,55066998749 | |||||
| 69,1685093594435 | 112,2962613819 | |||||
| 65,6374706822238 | 114,945962695954 | |||||
| 58,1400830647319 | 116,602276795217 | |||||
| 78,7915989931751 | 118,345653319227 | |||||
| 72,8914941375442 | 120,268015941527 | |||||
| 68,5054164049267 | 122,873146643073 | |||||
| 61,518705014158 | 125,557766944926 | |||||
| 78,1335731784645 | 127,189724815234 | |||||
| 78,3712332002471 | 130,437555629647 | |||||
| 74,0064716370768 | 132,01788788873 | |||||
| 67,4050246926091 | 135,318921692506 | |||||
| 85,8226347685586 | 137,102305690761 | |||||
| 83,194883045778 | 137,248484168378 | |||||
| 75,9200303847368 | 136,507419807885 | |||||
| 68,1230183586928 | 137,053716236591 | |||||
| 87,3372752177695 | 140,042390195142 | |||||
| 84,8945443615665 | 142,874608602934 | |||||
| 81,5863941417549 | 147,260748223411 | |||||
| 75,4413753502906 | 149,884930670532 | |||||
| 93,4285880304632 | 151,211266045902 | |||||
| 89,5715078811253 | 152,972460754738 | |||||
| 83,9502507313823 | 155,154623959009 | |||||
| 78,5186832147435 | 159,721827677609 | |||||
| 99,5712668155701 | 162,293164255201 | |||||
| 96,5246178722633 | 164,233751056557 | |||||
| 91,2884260850914 | 165,233709826198 | |||||
| 85,0629128312343 | 165,894254490476 | |||||
| 103,245514450378 | 168,818243314759 | |||||
| 101,464306327094 | 170,302019861189 | |||||
| 93,448754500595 | 170,518412604691 | |||||
| 86,6978732780597 | 171,44559835787 | |||||
| 106,096704118092 | 175,675134137059 | |||||
| 104,169282387472 | 180,115427725381 | |||||
| 98,4286143663242 | 182,973860207867 | |||||
| 93,9338216380859 | 185,824959013781 | |||||
| 112,356988777469 | 187,911635423744 | |||||
| 107,346302585979 | 189,892834106359 | |||||
| 103,195824208241 | 190,883162883682 | |||||
| 96,8527952828484 | 192,307347799297 | |||||
| 115,073115064688 | 195,729708746176 | |||||
| 112,438837972484 | 198,815615253369 | |||||
| 108,930227237007 | 202,418624128214 | |||||
| 102,31749056783 | 204,468265962759 | |||||
| 119,089070458272 | 204,889983330094 | |||||
| 115,866482036584 | 206,530285279943 | |||||
| 112,726044352273 | 209,086349307934 | |||||
| 107,822665120148 | 212,44246054199 | |||||
| 124,331462698487 | 217,012490547821 | |||||
| 122,620589240846 | 220,498361057115 | |||||
| 117,100246510859 | 222,853884309429 | |||||
| 112,385301044006 | 224,746897731868 | |||||
| 130,329423660117 | 227,790395142163 | |||||
| 129,542132283685 | 231,579638478334 | |||||
| 124,53648711341 | 233,973261182302 | |||||
| 120,501665861038 | 238,221475199817 | |||||
| 140,608330694059 | 240,896933126988 | |||||
| 136,790970307066 | 243,586476483567 | |||||
| 131,677048528135 | 245,967764990988 | |||||
| 125,148978967354 | 249,668591902067 | |||||
| 144,480036485479 | 253,684189954638 | |||||
| 142,624849862326 | 258,814358216492 | |||||
| 138,421236940235 | 260,441603126391 | |||||
| 134,058046826819 | 263,442458276599 | |||||
| 151,693002788131 | 268,162587887743 | |||||
| 150,170209738746 | 274,084910633232 | |||||
| 145,044687291824 | 277,417620161519 | |||||
| 138,014911519266 | 279,713345827467 | |||||
| 159,293081727329 | 283,689524849126 | |||||
| 157,237621698171 | 287,740324093576 | |||||
| 153,31320587926 | 290,992352107138 | |||||
| 148,160638120915 | 295,504246416138 | |||||
| 168,72344863903 | 300,745782365214 | |||||
| 166,703175036287 | 304,214392616152 | |||||
| 162,804331045101 | 308,33648336199 | |||||
| 155,08848699932 | 312,074684634534 |
| Zadanie | |||
| Wiedząc, że dla poniższych danych (z pominięciem ostatnich dwóch obserwacji) pominięciemzachodzi zależność | |||
| Y1t=f1(stała, Y2t, Y1,t-1, Xt-1) | |||
| Y2t=f2(stała, Y1t, Xt, Xt-1, t) | |||
| Korzystając z symulacji wyznaczyć mnożniki bezpośrenie i pośrednie oraz podać interpretacje | |||
| zaburzenie w 1980 roku (wartość zmiennej zaburzonej jest o 5% wieksza od wartości pierwotnej) | |||
| t | Y1t | Y2t | Xt |
| 1970 | 176 | 301 | 52 |
| 1971 | 185 | 317 | 52 |
| 1972 | 188 | 342 | 53 |
| 1973 | 198 | 356 | 53 |
| 1974 | 199 | 373 | 56 |
| 1975 | 201 | 381 | 59 |
| 1976 | 205 | 407 | 62 |
| 1977 | 211 | 432 | 66 |
| 1978 | 216 | 436 | 70 |
| 1979 | 214 | 438 | 70 |
| 1980 | 215 | 440 | 72 |
| 1981 | 220 | 444 | 73 |
| 1982 | 223 | 460 | 71 |
| 1983 | 224 | 480 | 65 |
| 1984 | 223 | 475 | 63 |
| 1985 | 224 | 483 | 57 |
| 1986 | 226 | 510 | 59 |
| 1987 | 225 | 501 | 60 |
| 1988 | 224 | 514 | 61 |
| 1989 | 226 | 520 | 61 |
| 1990 | 227 | 524 | 62 |
| 1991 | 230 | 538 | 65 |
| 1992 | 232 | 543 | 64 |
| 1993 | 235 | 560 | 63 |
| Yt | Xt | dane kwartalne | ||||
| 211,8480 | 64,3302 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 211,8168 | 63,0964 | Yt | 2 | - | ||
| 213,6269 | 63,7079 | Xt | 3 | |||
| 218,209860831419 | 63,647516150977 | |||||
| 221,54490774353 | 64,3341551839518 | |||||
| 220,563344978496 | 65,3720822556648 | |||||
| 223,73141586578 | 64,9876009039555 | |||||
| 228,25079156795 | 67,2276142726779 | |||||
| 227,823374423613 | 66,4035938109282 | |||||
| 228,631730515151 | 65,670479768662 | |||||
| 231,979628110254 | 65,6369911268063 | |||||
| 234,256856217184 | 66,4981189571774 | |||||
| 236,709718042917 | 67,5131846543337 | |||||
| 239,844645963447 | 69,4473667198255 | |||||
| 241,159181907803 | 68,4970883087425 | |||||
| 243,395107323433 | 67,6871349012007 | |||||
| 245,785093316272 | 67,6702475794981 | |||||
| 247,138070299443 | 67,7135961142604 | |||||
| 249,328214842795 | 68,1820645735916 | |||||
| 251,402572625214 | 69,4677745198926 | |||||
| 251,639253333474 | 69,4741423131502 | |||||
| 254,65609703185 | 70,5941190604546 | |||||
| 258,858119328485 | 69,2683711322848 | |||||
| 261,995993769394 | 70,5544670481057 | |||||
| 262,35025476315 | 68,1914144612685 | |||||
| 264,882853332967 | 69,8342560108627 | |||||
| 265,75874475512 | 67,6735101363633 | |||||
| 269,584666127906 | 68,6364510064594 | |||||
| 271,757881000907 | 69,5798175432581 | |||||
| 273,465240418142 | 71,4855055549458 | |||||
| 275,801602109168 | 71,3227089501476 | |||||
| 277,942793932358 | 71,0944844229354 | |||||
| 279,956156365689 | 70,1068506701099 | |||||
| 281,399837133287 | 70,6683990059281 | |||||
| 286,234172471525 | 72,2939376205955 | |||||
| 289,572987955025 | 73,8667059021733 | |||||
| 292,779101155564 | 75,0967956165144 | |||||
| 294,125845338374 | 76,0763811780929 | |||||
| 296,402920492987 | 75,7258643291847 | |||||
| 298,165773588219 | 76,3953602605543 | |||||
| 299,167663740974 | 77,9900352455248 | |||||
| 301,815761481604 | 75,5773598841967 | |||||
| 306,863203965993 | 77,7504904404843 | |||||
| 307,26310130516 | 76,3773442244931 | |||||
| 308,982165635316 | 76,4061161124511 | |||||
| 311,848071307825 | 76,1386864579668 | |||||
| 314,846112485297 | 76,6999465094135 | |||||
| 315,830753108144 | 77,4459452714893 | |||||
| 319,595250472934 | 77,7450083512732 | |||||
| 321,170081071091 | 76,4212001254553 | |||||
| 322,512987429235 | 75,9751535389028 | |||||
| 325,629845429962 | 75,7967658446139 | |||||
| 330,058800584785 | 77,3259421278095 | |||||
| 331,545472059643 | 77,4235585350703 | |||||
| 333,863799980202 | 78,2885204439693 | |||||
| 335,376813765251 | 79,4293434457377 | |||||
| 337,572396439275 | 80,6290848381931 | |||||
| 339,58191167398 | 79,7509583316626 | |||||
| 344,135462119406 | 81,0230275944742 | |||||
| 346,633424798887 | 81,4378898479921 | |||||
| 350,823490946855 | 81,7137395056042 | |||||
| 353,095268173034 | 82,3421790894257 | |||||
| 353,719796385861 | 81,9137692446809 | |||||
| 355,877788369936 | 81,6129442969835 | |||||
| 361,839115326932 | 81,5613559634076 | |||||
| 362,761123509932 | 82,7146786145442 | |||||
| 364,167261962589 | 84,1344929598065 | |||||
| 367,262149684568 | 83,5469774635463 | |||||
| 370,818049878945 | 84,6102963895155 | |||||
| 373,303557448664 | 83,5040021197634 | |||||
| 374,760465006463 | 83,6532949079798 | |||||
| 375,853092665476 | 83,5820477936118 | |||||
| 379,32846088577 | 83,1330215039695 | |||||
| 384,633688641053 | 84,4346704092662 | |||||
| 385,673404668893 | 82,2644661789549 | |||||
| 389,855646593862 | 82,9242231472544 | |||||
| 389,692177274846 | 82,0919619749113 | |||||
| 393,072625749352 | 82,1247470908232 | |||||
| 395,085751135923 | 81,7875669265988 | |||||
| 398,347926041544 | 82,2303285808838 | |||||
| 401,460899761073 | 84,7207506664337 | |||||
| 404,087580359152 | 84,771910655449 | |||||
| 408,399361879651 | 85,2397969425676 | |||||
| 408,780375246355 | 84,1927809231453 | |||||
| 410,855268092894 | 84,2523035978822 | |||||
| 415,082525479341 | 85,0951874069476 | |||||
| 420,463007674995 | 85,8453660795989 | |||||
| 421,950343658796 | 85,0618517582271 | |||||
| 423,745336580046 | 86,0861685732491 | |||||
| 427,50358784136 | 88,6538003128227 | |||||
| 430,91538023783 | 89,4806404393052 | |||||
| 434,738929670992 | 91,2221546867106 | |||||
| 438,000799758691 | 90,6712403499245 | |||||
| 440,367186785561 | 91,6424865630993 | |||||
| 444,060835886416 | 91,2972817618047 | |||||
| 448,012624841518 | 91,8057951322082 | |||||
| 449,732392024091 | 93,3465438084673 | |||||
| 453,654454455103 | 92,0046628532286 | |||||
| 456,674810417479 | 92,0625681133586 |
| Zadanie |
| Dokaonaj identyfikacji modelu ARMA (do p=3 i q=3) dla poniższego szeregu |
| Yt |
| 1,6934723 |
| 1,3040391 |
| 1,2957693 |
| 0,40598454 |
| 0,12425803 |
| -0,35923848 |
| -0,84672123 |
| -2,2353983 |
| -2,3881432 |
| -0,44474021 |
| -0,22861908 |
| -1,1653847 |
| 0,87295983 |
| 1,549451 |
| 0,0045300819 |
| 0,75730961 |
| -0,65756099 |
| 1,4759265 |
| 1,0316313 |
| 0,75066231 |
| 0,91297555 |
| -0,42199815 |
| 0,73816567 |
| 1,1714058 |
| -0,44137184 |
| -0,13920141 |
| -1,0838609 |
| -0,90986252 |
| -1,6920258 |
| -1,3892181 |
| -0,52497006 |
| 0,97455853 |
| 0,36998309 |
| -0,89579304 |
| -0,41085776 |
| -1,1657919 |
| -1,2285244 |
| 1,2487575 |
| 0,91634723 |
| -0,7391479 |
| -0,50455993 |
| -0,71880353 |
| -1,0394617 |
| -0,57293629 |
| -0,56069655 |
| -0,084474084 |
| 1,6517755 |
| 0,49361433 |
| -0,49978354 |
| 0,69691826 |
| 1,25749 |
| 1,0078869 |
| 0,33828185 |
| -1,1066812 |
| 0,11917161 |
| 0,069320637 |
| 0,028094573 |
| -0,39130732 |
| 0,21510975 |
| -0,045189908 |
| -0,70670025 |
| -1,7021921 |
| -1,7652484 |
| 1,2381812 |
| 2,991105 |
| 0,031365529 |
| -0,62335848 |
| 0,0068517728 |
| -0,40786049 |
| 1,6153633 |
| 1,4774454 |
| -0,33997687 |
| -1,5568899 |
| -0,52830623 |
| 0,11398371 |
| -1,3390133 |
| -0,011061902 |
| 0,39418065 |
| 1,3515234 |
| 0,42910833 |
| 0,39880045 |
| -0,39446867 |
| -0,31194829 |
| 1,2199685 |
| 2,0173667 |
| 0,79197521 |
| 2,5886134 |
| 1,1869116 |
| 1,2439476 |
| 0,8910753 |
| -0,20819459 |
| 1,6781688 |
| 1,2091766 |
| -0,12569695 |
| -0,31683863 |
| 0,23609192 |
| 0,15726379 |
| 0,061203814 |
| -0,13616016 |
| -1,0458975 |
| -0,50882911 |
| -1,5559672 |
| -0,92939618 |
| 0,011938302 |
| 0,38218234 |
| 1,087337 |
| -0,71195533 |
| -1,7987526 |
| 1,4096025 |
| 3,7122512 |
| 2,2676118 |
| -0,11028947 |
| 0,30571115 |
| 0,48775736 |
| -1,9712641 |
| -0,96491056 |
| -0,087767014 |
| 0,39285011 |
| 0,31896218 |
| -3,4566775 |
| -2,8829127 |
| -2,0335651 |
| -1,5263368 |
| -2,25344 |
| -1,1941915 |
| -1,0562377 |
| 0,12616291 |
| -0,40455238 |
| 0,23661362 |
| -1,0959297 |
| -2,6059402 |
| -1,9498709 |
| 0,11495432 |
| 1,4547454 |
| -0,037470351 |
| 1,2522591 |
| 0,65708236 |
| 0,061348921 |
| -0,22939718 |
| -0,7010939 |
| -0,016150798 |
| 0,70434304 |
| 0,079458575 |
| -2,7942833 |
| 0,81050041 |
| 0,12048303 |
| 1,4439509 |
| 1,9776301 |
| -2,1677575 |
| -1,3431805 |
| 0,24840296 |
| 0,91752415 |
| 0,98825638 |
| 0,87359224 |
| 0,57943692 |
| 0,55435587 |
| 1,8796285 |
| 1,3521435 |
| 0,080337556 |
| -0,07878021 |
| 0,63656413 |
| 0,27836157 |
| -0,81148038 |
| -1,4377638 |
| -0,22233395 |
| 1,1266389 |
| 1,7949593 |
| 1,5545227 |
| -0,2807447 |
| 0,45403418 |
| -0,59374536 |
| -0,62674417 |
| -1,4157555 |
| 0,65386369 |
| 1,1158787 |
| 1,1527837 |
| 0,33683976 |
| 0,24039565 |
| -0,9271278 |
| -1,8445615 |
| -1,6846627 |
| 1,2875536 |
| 1,2683868 |
| -0,13535423 |
| -0,66288293 |
| -1,3117772 |
| 0,77083395 |
| 1,630591 |
| 0,94268342 |
| 0,67212219 |
| 1,5195853 |
| 1,7819171 |
| 2,0285673 |
| -0,26952489 |
| -1,1386903 |
| 0,8849238 |
| 1,695147 |
| 1,6399814 |
| 0,68213947 |
| 0,32339625 |
| Yt | Xt | dane kwartalne | ||||
| 58,9525 | 32,0999 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 60,7660 | 31,4629 | Yt | 2 | |||
| 59,3627 | 30,8625 | Xt | 1 | - | ||
| 60,5059751488873 | 30,7809159017464 | |||||
| 62,3259504905013 | 30,31269764575 | |||||
| 63,7019692720194 | 33,016869387278 | |||||
| 66,833653485933 | 34,4391346844703 | |||||
| 68,4722888818674 | 35,8143155661626 | |||||
| 71,6762777363374 | 36,8323874241993 | |||||
| 71,2597415622297 | 36,2192389298943 | |||||
| 70,7357824443257 | 36,3026203649533 | |||||
| 70,9642415190403 | 35,1673284495957 | |||||
| 73,0683366775769 | 36,0790682382241 | |||||
| 74,5022227411874 | 35,5197222286449 | |||||
| 76,1717928196314 | 36,5523603415995 | |||||
| 77,7548259211096 | 37,9432552600683 | |||||
| 78,6808191863723 | 37,0007423387987 | |||||
| 79,7817094483393 | 36,9592241468597 | |||||
| 81,7113923589274 | 39,1608285524277 | |||||
| 82,9521423567422 | 37,9021987629976 | |||||
| 81,7985559163561 | 37,9243428704547 | |||||
| 82,9434558144838 | 39,048733927732 | |||||
| 85,2113222590907 | 39,9483768579493 | |||||
| 87,2335846090354 | 41,5500154047932 | |||||
| 88,1028171507158 | 41,2655770551936 | |||||
| 89,5655532068981 | 42,0971331884836 | |||||
| 90,891273094526 | 42,339263267538 | |||||
| 91,3009366945095 | 42,1145088327829 | |||||
| 91,8709746464429 | 42,9887085255127 | |||||
| 93,7849911119979 | 42,8233959641862 | |||||
| 95,377964286784 | 42,2358879660276 | |||||
| 95,5627210923933 | 41,3193986603726 | |||||
| 98,7351862125735 | 44,1025662592319 | |||||
| 98,016885235401 | 42,6857383863686 | |||||
| 97,9787717997169 | 42,699207016153 | |||||
| 102,561002500517 | 43,3026531753713 | |||||
| 103,680297710312 | 43,3704716503321 | |||||
| 102,626214591754 | 42,6644847046133 | |||||
| 105,167516655525 | 43,8783501532547 | |||||
| 107,384395584789 | 44,8784961885958 | |||||
| 109,480971098181 | 46,1762554370708 | |||||
| 110,044382139175 | 46,4707576318774 | |||||
| 113,314392098262 | 46,3521077357163 | |||||
| 114,184496441013 | 48,3715516171504 | |||||
| 115,21592085273 | 49,0478669263447 | |||||
| 114,82599765649 | 48,0720507864432 | |||||
| 116,359317917455 | 47,7845853049835 | |||||
| 116,889684195353 | 48,0803515641525 | |||||
| 120,316022873319 | 47,9069115291132 | |||||
| 120,630751618145 | 47,0908264786283 | |||||
| 119,370616109783 | 46,6799816809432 | |||||
| 123,591091382949 | 47,0706528144261 | |||||
| 126,318826164667 | 46,8382861786556 | |||||
| 128,71854174405 | 49,9743998331981 | |||||
| 129,240390950528 | 49,0578351739501 | |||||
| 129,805003971233 | 48,2323473359934 | |||||
| 132,719308491068 | 49,0700137207408 | |||||
| 133,488369051838 | 50,9039467705266 | |||||
| 136,134618777119 | 50,7207973883921 | |||||
| 136,89531961506 | 49,7489394588843 | |||||
| 136,981258797254 | 50,9955074836314 | |||||
| 139,621437094001 | 52,2790775985288 | |||||
| 143,368556555908 | 53,1864186722827 | |||||
| 144,574852946097 | 53,9046148534303 | |||||
| 145,025456830736 | 52,6894404793802 | |||||
| 144,799585644719 | 52,4493090571387 | |||||
| 146,353196883428 | 50,6829255131251 | |||||
| 151,173528076406 | 52,8372524804531 | |||||
| 149,520157867439 | 51,618292578827 | |||||
| 154,498754878444 | 54,5226954466898 | |||||
| 153,583273034288 | 54,4744240902403 | |||||
| 155,554288098817 | 53,7954469814098 | |||||
| 158,176784862792 | 53,890501024721 | |||||
| 161,866129713397 | 53,4078999936796 | |||||
| 162,34779358131 | 53,45989090671 | |||||
| 162,35982172819 | 51,9285934278567 | |||||
| 162,8599960648 | 52,5185026727768 | |||||
| 167,275475680934 | 54,4542517179587 | |||||
| 166,755975959136 | 53,5948083188328 | |||||
| 167,521795939512 | 54,9952408040152 | |||||
| 171,382598818195 | 54,6287607148688 | |||||
| 171,061312510997 | 54,8873430778462 | |||||
| 174,803826312751 | 54,5677202081499 | |||||
| 177,086169297938 | 56,085454926085 | |||||
| 178,268459236424 | 56,9850658951352 | |||||
| 183,154971748954 | 58,4271385627902 | |||||
| 184,815966971009 | 59,7081257772767 | |||||
| 183,102708739944 | 60,4040164339037 | |||||
| 185,508574165526 | 59,0526215243576 | |||||
| 189,283869629504 | 60,0557148417661 | |||||
| 189,514706175453 | 59,3998835597628 | |||||
| 189,740527454645 | 58,8945086394922 | |||||
| 194,492100588793 | 60,8793781472202 | |||||
| 197,173889375764 | 60,1609405829493 | |||||
| 198,506357344905 | 62,2328701243321 | |||||
| 200,656318482407 | 63,2702156324732 | |||||
| 202,425302905173 | 62,054423863441 | |||||
| 202,862314035829 | 60,4874873692843 | |||||
| 203,629854042904 | 61,2569251910366 | |||||
| 206,019500691555 | 61,8873090718227 |
| Zadanie |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich dwóch obserwacji) |
| dokonać wyrównania wykładniczego |
| oraz wyrównać szereg za pomocą sredniej 3-wyrazowj. |
| Obliczyć prognozy. Która metoda dała lepsze wyniki? |
| Pt |
| 584,5 |
| 585 |
| 589 |
| 609 |
| 604 |
| 608 |
| 618 |
| 623 |
| 614,5 |
| 628 |
| 640 |
| 648 |
| 613 |
| 602,5 |
| 622 |
| 644 |
| 657 |
| 671,5 |
| 705 |
| 688 |
| 690 |
| 690 |
| 752,5 |
| 763 |
| 770 |
| 773,5 |
| 778,5 |
| 790,5 |
| 785 |
| 776 |
| 770 |
| 800 |
| 800 |
| 804,5 |
| 779 |
| 775 |
| 765 |
| 775 |
| 725 |
| 760 |
| 794 |
| 776 |
| 793 |
| 765 |
| 680 |
| 690 |
| 710 |
| 615 |
| 614 |
| 675 |
| Yt | Xt | dane kwartalne | ||||
| 48,1183107138122 | 64,1442 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 44,6353997167258 | 65,9714 | Yt | 1 | 1 | ||
| 39,0506105076807 | 67,1621 | Xt | - | |||
| 33,4033278345713 | 68,190702584866 | |||||
| 51,9950409479241 | 69,6209053537098 | |||||
| 48,9929799569888 | 72,7457716429085 | |||||
| 43,4407589077525 | 76,0440236799703 | |||||
| 37,2680251252945 | 78,1779031828218 | |||||
| 58,2534578266532 | 80,3016421194227 | |||||
| 53,9494482767622 | 82,0676597865827 | |||||
| 49,7315457144966 | 84,0730730455222 | |||||
| 42,6088408999317 | 84,1918726081281 | |||||
| 59,9825558408614 | 85,7002070858551 | |||||
| 56,9810533988051 | 87,2920544996764 | |||||
| 53,0352352822315 | 90,5910444154961 | |||||
| 47,6299567411805 | 93,3200004078775 | |||||
| 68,350169487491 | 94,8349824377403 | |||||
| 63,67413466217 | 97,1279910557192 | |||||
| 57,8746208435369 | 102,003502552763 | |||||
| 52,7447622106246 | 104,507854854094 | |||||
| 71,3282305947596 | 106,221826405942 | |||||
| 67,274094326561 | 105,707671261333 | |||||
| 60,0636818820922 | 105,79930506829 | |||||
| 53,1345066887794 | 107,733184029612 | |||||
| 72,2390923307317 | 110,55066998749 | |||||
| 69,1685093594435 | 112,2962613819 | |||||
| 65,6374706822238 | 114,945962695954 | |||||
| 58,1400830647319 | 116,602276795217 | |||||
| 78,7915989931751 | 118,345653319227 | |||||
| 72,8914941375442 | 120,268015941527 | |||||
| 68,5054164049267 | 122,873146643073 | |||||
| 61,518705014158 | 125,557766944926 | |||||
| 78,1335731784645 | 127,189724815234 | |||||
| 78,3712332002471 | 130,437555629647 | |||||
| 74,0064716370768 | 132,01788788873 | |||||
| 67,4050246926091 | 135,318921692506 | |||||
| 85,8226347685586 | 137,102305690761 | |||||
| 83,194883045778 | 137,248484168378 | |||||
| 75,9200303847368 | 136,507419807885 | |||||
| 68,1230183586928 | 137,053716236591 | |||||
| 87,3372752177695 | 140,042390195142 | |||||
| 84,8945443615665 | 142,874608602934 | |||||
| 81,5863941417549 | 147,260748223411 | |||||
| 75,4413753502906 | 149,884930670532 | |||||
| 93,4285880304632 | 151,211266045902 | |||||
| 89,5715078811253 | 152,972460754738 | |||||
| 83,9502507313823 | 155,154623959009 | |||||
| 78,5186832147435 | 159,721827677609 | |||||
| 99,5712668155701 | 162,293164255201 | |||||
| 96,5246178722633 | 164,233751056557 | |||||
| 91,2884260850914 | 165,233709826198 | |||||
| 85,0629128312343 | 165,894254490476 | |||||
| 103,245514450378 | 168,818243314759 | |||||
| 101,464306327094 | 170,302019861189 | |||||
| 93,448754500595 | 170,518412604691 | |||||
| 86,6978732780597 | 171,44559835787 | |||||
| 106,096704118092 | 175,675134137059 | |||||
| 104,169282387472 | 180,115427725381 | |||||
| 98,4286143663242 | 182,973860207867 | |||||
| 93,9338216380859 | 185,824959013781 | |||||
| 112,356988777469 | 187,911635423744 | |||||
| 107,346302585979 | 189,892834106359 | |||||
| 103,195824208241 | 190,883162883682 | |||||
| 96,8527952828484 | 192,307347799297 | |||||
| 115,073115064688 | 195,729708746176 | |||||
| 112,438837972484 | 198,815615253369 | |||||
| 108,930227237007 | 202,418624128214 | |||||
| 102,31749056783 | 204,468265962759 | |||||
| 119,089070458272 | 204,889983330094 | |||||
| 115,866482036584 | 206,530285279943 | |||||
| 112,726044352273 | 209,086349307934 | |||||
| 107,822665120148 | 212,44246054199 | |||||
| 124,331462698487 | 217,012490547821 | |||||
| 122,620589240846 | 220,498361057115 | |||||
| 117,100246510859 | 222,853884309429 | |||||
| 112,385301044006 | 224,746897731868 | |||||
| 130,329423660117 | 227,790395142163 | |||||
| 129,542132283685 | 231,579638478334 | |||||
| 124,53648711341 | 233,973261182302 | |||||
| 120,501665861038 | 238,221475199817 | |||||
| 140,608330694059 | 240,896933126988 | |||||
| 136,790970307066 | 243,586476483567 | |||||
| 131,677048528135 | 245,967764990988 | |||||
| 125,148978967354 | 249,668591902067 | |||||
| 144,480036485479 | 253,684189954638 | |||||
| 142,624849862326 | 258,814358216492 | |||||
| 138,421236940235 | 260,441603126391 | |||||
| 134,058046826819 | 263,442458276599 | |||||
| 151,693002788131 | 268,162587887743 | |||||
| 150,170209738746 | 274,084910633232 | |||||
| 145,044687291824 | 277,417620161519 | |||||
| 138,014911519266 | 279,713345827467 | |||||
| 159,293081727329 | 283,689524849126 | |||||
| 157,237621698171 | 287,740324093576 | |||||
| 153,31320587926 | 290,992352107138 | |||||
| 148,160638120915 | 295,504246416138 | |||||
| 168,72344863903 | 300,745782365214 | |||||
| 166,703175036287 | 304,214392616152 | |||||
| 162,804331045101 | 308,33648336199 | |||||
| 155,08848699932 | 312,074684634534 |
| Zadanie |
| Oblicz prognozę na okres 56, 57, 58 z najlepszego modelu średniej ruchomej (3, 6, 10 - wyrazowej). |
| Policz błedy ex post. |
| Yt |
| 261081,81 |
| 253499,15 |
| 337930,85 |
| 336088,22 |
| 404564,99 |
| 458250,25 |
| 642775,85 |
| 633534,11 |
| 657441,68 |
| 837428,67 |
| 767538,68 |
| 1294972,53 |
| 1028150,13 |
| 1091291,53 |
| 1462652,11 |
| 1483307,18 |
| 1666981,67 |
| 1674585,3 |
| 1915321,56 |
| 2088865,45 |
| 2177568 |
| 2709432,58 |
| 2583638,05 |
| 3158578,86 |
| 5001106,87 |
| 5136984,68 |
| 5157690,14 |
| 5258448 |
| 5631662,3 |
| 5745434,49 |
| 5795389,54 |
| 6210795,52 |
| 6589431,28 |
| 6618815,45 |
| 6677550,46 |
| 6608391,84 |
| 6831286,28 |
| 6951894,14 |
| 7211488,13 |
| 7137416 |
| 7851701,86 |
| 8162412,81 |
| 8664961,61 |
| 9137088,98 |
| 9332866,27 |
| 9517383,54 |
| 9851180,65 |
| 10392635,16 |
| 10478127,66 |
| 10728541,01 |
| 10974625,41 |
| 11410564 |
| 11734090,66 |
| 12322070,54 |
| 13022860,29 |
| 13717994,75 |
| 13938299,17 |
| 14309128,42 |
| Yt | Xt | |||||
| 461,6758 | 92,8089 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 464,7396 | 93,2188 | Yt | 2 | - | 2 | |
| 468,0337 | 93,7363 | Xt | ||||
| 469,683754317101 | 94,5209007107899 | |||||
| 471,807422037701 | 93,1018689408048 | |||||
| 477,215643019114 | 93,4341092132529 | |||||
| 478,534285055437 | 91,0709569893605 | |||||
| 484,210906167517 | 93,1009288683672 | |||||
| 485,675526643443 | 92,2222154620146 | |||||
| 487,382032028823 | 94,6455380860483 | |||||
| 491,83087751273 | 94,9845555251648 | |||||
| 495,01892016423 | 96,6620072010269 | |||||
| 499,373035946554 | 96,3759640810586 | |||||
| 501,759859377655 | 97,8403659120161 | |||||
| 503,986810786108 | 98,4787439225235 | |||||
| 506,840020428844 | 98,6780377031596 | |||||
| 510,2309120682 | 97,5155763865655 | |||||
| 513,840566531338 | 96,387465997039 | |||||
| 516,387276469953 | 97,8610915732651 | |||||
| 518,630204397625 | 96,5077886230842 | |||||
| 523,46117996955 | 99,1929863087306 | |||||
| 525,266674242 | 98,5352086883837 | |||||
| 528,392892524648 | 99,1505842498709 | |||||
| 532,989211575903 | 98,8956743196786 | |||||
| 534,999677735329 | 100,23860556106 | |||||
| 538,438269965861 | 99,6512093386711 | |||||
| 543,185290870196 | 100,423793341452 | |||||
| 546,258435290642 | 99,1473970284058 | |||||
| 547,912400289126 | 99,7051740545854 | |||||
| 552,441088294895 | 99,6382822784411 | |||||
| 557,465190643219 | 101,292670405603 | |||||
| 560,137783068299 | 101,188619156538 | |||||
| 563,067133795121 | 101,818178075569 | |||||
| 565,25249425628 | 103,599376318739 | |||||
| 567,136817804747 | 104,58269301448 | |||||
| 571,149864539803 | 104,955262390644 | |||||
| 575,716872231383 | 104,698716314047 | |||||
| 579,716240476577 | 103,55354153413 | |||||
| 583,691242627834 | 104,744041489977 | |||||
| 585,447312926568 | 105,023348240413 | |||||
| 586,761106791232 | 104,463747908456 | |||||
| 593,697114248028 | 105,688719710048 | |||||
| 597,191056472461 | 106,145958521488 | |||||
| 599,981118437246 | 105,594837296365 | |||||
| 604,481887984993 | 107,789329721892 | |||||
| 608,966487022819 | 107,860690289936 | |||||
| 612,512179905322 | 109,49101466025 | |||||
| 615,213964716764 | 109,489751404777 | |||||
| 616,532566721784 | 108,241892323432 | |||||
| 621,688138025782 | 109,814147115786 | |||||
| 625,717145875254 | 108,735120397124 | |||||
| 628,093489472351 | 109,641149948036 | |||||
| 630,945112069779 | 110,136511659605 | |||||
| 633,929189568926 | 111,14477906671 | |||||
| 637,33872914974 | 110,383568854971 | |||||
| 640,776288460866 | 110,910529586572 | |||||
| 646,221702048468 | 111,10288555375 | |||||
| 649,070893140264 | 111,091664992602 | |||||
| 652,082998660817 | 110,517725243632 | |||||
| 655,715604611458 | 110,940230057573 | |||||
| 661,710021296761 | 112,17784561487 | |||||
| 664,456341795125 | 112,293015898955 | |||||
| 666,449161398062 | 113,477018802215 | |||||
| 670,394762880501 | 113,290648808263 | |||||
| 675,525193390865 | 115,214056626657 | |||||
| 677,623967359257 | 113,513730520696 | |||||
| 682,704938890261 | 112,724998590832 | |||||
| 683,923394191613 | 112,24610684446 | |||||
| 688,843961045362 | 114,718928264232 | |||||
| 692,187984889822 | 114,104482120134 | |||||
| 695,421574186415 | 114,583294594472 | |||||
| 700,132278967939 | 114,940165199324 | |||||
| 703,107917009696 | 113,617607593841 | |||||
| 703,099874585643 | 112,609615956592 | |||||
| 708,303319758738 | 113,822080407902 | |||||
| 715,741059335506 | 115,242919553741 | |||||
| 718,124395509707 | 114,024644618671 | |||||
| 722,437548585317 | 117,053611017611 | |||||
| 726,375313354508 | 116,803137187181 | |||||
| 729,379006269475 | 116,853350412576 | |||||
| 731,582450745193 | 117,517064241435 | |||||
| 737,891759268952 | 118,529122655341 | |||||
| 741,748972859425 | 118,279835048654 | |||||
| 745,970396686367 | 117,211208482373 | |||||
| 748,230697425445 | 117,751571921189 | |||||
| 749,063764917592 | 117,118995879814 | |||||
| 755,832572298786 | 117,738626995752 | |||||
| 759,323698928633 | 116,544523276732 | |||||
| 762,952387894656 | 117,737455216475 | |||||
| 766,173179054631 | 116,443350235402 | |||||
| 770,765090857028 | 117,752177074378 | |||||
| 775,166122849917 | 118,18823797939 | |||||
| 779,002024898916 | 117,421349660806 | |||||
| 782,64657847342 | 118,276880741506 | |||||
| 786,940821283771 | 119,924473821418 | |||||
| 789,152720369834 | 121,081925965283 | |||||
| 795,472947022375 | 122,490914173822 | |||||
| 803,684460217286 | 125,227522946977 | |||||
| 806,484971949208 | 125,335455121974 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 119,5 | |
| 132 | |
| 136 | |
| 143 | |
| 141 | |
| 139 | |
| 135,5 | |
| 132 | |
| 128,5 | |
| 129 | |
| 132,5 | |
| 141 | |
| 135 | |
| 141,5 | |
| 133,5 | |
| 131 | |
| 129 | |
| 128,5 | |
| 119 | |
| 113 | |
| 105 | |
| 93,4 | |
| 92 | |
| 87,1 | |
| 94,2 | |
| 92,7 | |
| 95,5 | |
| 92 | |
| 95,5 | |
| 95,1 | |
| 104 | |
| 108 | |
| 114 | |
| 112,5 | |
| 109 | |
| 112,5 | |
| 113 | |
| 111 | |
| 115 | |
| 115 | |
| 123 | |
| 121 | |
| 116,5 | |
| 117 | |
| 115,5 | |
| 113 | |
| 118,5 | |
| 126 | |
| 122 | |
| 123 |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | 1 | + | ||
| 12,3805 | 25,9273 | Xt | 3 | |||
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Wintersa |
| b) | policzyć prognozy oraz błędy prognoz |
| Yt | |
| 538 | |
| 546 | |
| 555 | |
| 566 | |
| 573 | |
| 576 | |
| 577 | |
| 579 | |
| 586 | |
| 585 | |
| 572 | |
| 564 | |
| 574 | |
| 579 | |
| 586 | |
| 591 | |
| 594 | |
| 595 | |
| 596 | |
| 596 | |
| 598 | |
| 594 | |
| 583 | |
| 575 | |
| 585 | |
| 573 | |
| 576 | |
| 581 | |
| 586 | |
| 588 | |
| 586 | |
| 586 | |
| 586 | |
| 585 | |
| 580 | |
| 568 | |
| 517 | |
| 514 | |
| 515 | |
| 518 | |
| 519 | |
| 522 | |
| 521 | |
| 521 | |
| 519 | |
| 518 | |
| 512 | |
| 503 | |
| 491 | |
| 487 | |
| 482 | |
| 482 | |
| 481 | |
| 480 | |
| 477 | |
| 473 | |
| 469 | |
| 469 | |
| 467 |
| Yt | Xt | dane kwartalne | ||||
| 20,1127432256159 | 25,4327 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 20,684535774468 | 24,1043 | Yt | + | 3 | ||
| 26,8776559015158 | 15,6247 | Xt | 0 | |||
| 20,9937015411991 | 25,7428290413533 | |||||
| 21,9107551616107 | 25,4134602107025 | |||||
| 24,0340909764375 | 22,1911901999061 | |||||
| 29,833763790308 | 13,1606901302175 | |||||
| 22,3175596971194 | 24,0207330284325 | |||||
| 23,5741947621081 | 25,7876517282962 | |||||
| 25,0091875525615 | 23,0042830396848 | |||||
| 33,0139235606183 | 13,716866308029 | |||||
| 27,6501690333759 | 22,1946313571301 | |||||
| 27,1686563424295 | 22,1683304941821 | |||||
| 30,4406889833579 | 18,1123605692742 | |||||
| 37,0689633410425 | 10,2096794660749 | |||||
| 29,1358234337453 | 22,807562633373 | |||||
| 30,1417400082239 | 25,4524886939294 | |||||
| 29,9050445876062 | 24,4852755402514 | |||||
| 32,5440754981415 | 18,6072010398657 | |||||
| 25,570279783942 | 29,7035736775589 | |||||
| 25,8670810870127 | 29,7982369482151 | |||||
| 31,6951989003955 | 22,1635628073411 | |||||
| 41,3546739390274 | 7,60858723835225 | |||||
| 35,7570263657822 | 14,8219330547566 | |||||
| 35,5797705917128 | 15,2895643730935 | |||||
| 36,8605516836467 | 13,7509632476687 | |||||
| 41,9319748875703 | 9,00383326048572 | |||||
| 30,9202843132245 | 23,9009662938754 | |||||
| 30,0716352082217 | 28,5761961357634 | |||||
| 28,7521098453657 | 27,3692441527337 | |||||
| 35,8871466410647 | 18,2005141221868 | |||||
| 28,5487025679899 | 27,4085028580385 | |||||
| 28,3259688940063 | 25,1958418628936 | |||||
| 33,9601646527457 | 20,524394408395 | |||||
| 44,0694871532561 | 8,48697337682783 | |||||
| 35,8741162571666 | 19,614202435369 | |||||
| 35,2816270731357 | 20,8284478574454 | |||||
| 39,1839343352869 | 17,5486343800805 | |||||
| 46,7164965254407 | 6,87441193642793 | |||||
| 39,2790977073096 | 16,8055881562123 | |||||
| 37,7904573766526 | 19,3680703071545 | |||||
| 38,6783764085632 | 18,6492831508561 | |||||
| 43,0195493944622 | 14,1440897649308 | |||||
| 33,5609564092565 | 27,9631887881187 | |||||
| 32,2595471018711 | 29,9551212725523 | |||||
| 34,5372755061167 | 26,0660241267768 | |||||
| 42,7647540561202 | 14,0771294575458 | |||||
| 35,6265114808997 | 23,7255854179742 | |||||
| 38,6913107815599 | 22,5551201569675 | |||||
| 42,2299506615262 | 18,3019653749712 | |||||
| 50,968512975726 | 7,46873645868318 | |||||
| 45,6308333002696 | 16,824009496419 | |||||
| 43,6889712964152 | 19,2212523814556 | |||||
| 47,1278168899176 | 16,9113952635518 | |||||
| 52,4382118072217 | 7,75820527837286 | |||||
| 44,7789079557179 | 18,9423727082 | |||||
| 41,7427600882115 | 23,1369115825844 | |||||
| 41,4431925708859 | 23,608323094755 | |||||
| 45,7899755469526 | 16,5631965272821 | |||||
| 38,6278126203748 | 28,7166236583718 | |||||
| 38,7892597416758 | 28,7312209788411 | |||||
| 41,0694755072774 | 23,072292273611 | |||||
| 52,5162779393891 | 9,10296875682071 | |||||
| 48,4139183731503 | 15,7141869646632 | |||||
| 47,5983953902644 | 15,8714272623225 | |||||
| 48,8777353856598 | 13,9929153515191 | |||||
| 53,845677273768 | 8,6723800263403 | |||||
| 43,8743613465002 | 22,8856842257773 | |||||
| 41,3733012969048 | 25,3930527375374 | |||||
| 43,0889587454245 | 23,0060685768603 | |||||
| 52,2681511430237 | 12,9275622591928 | |||||
| 46,5889247802472 | 22,7618378955342 | |||||
| 42,7113736952779 | 24,3695345995812 | |||||
| 44,9765026631449 | 21,7019012533492 | |||||
| 51,4068408723277 | 12,2260608657356 | |||||
| 46,1191480548259 | 22,1165862571627 | |||||
| 44,7739326417791 | 23,0212832322982 | |||||
| 48,0130037549099 | 20,5348255402308 | |||||
| 55,5216909744394 | 10,7759659553009 | |||||
| 48,3087952206135 | 23,2323025422737 | |||||
| 49,2080046046366 | 24,5091147078671 | |||||
| 50,6569415589217 | 21,865611244541 | |||||
| 58,1291762731406 | 11,8844747541853 | |||||
| 49,7233393801225 | 22,7551094866095 | |||||
| 48,4975476846585 | 24,2848478998085 | |||||
| 48,8054581789456 | 23,415858101745 | |||||
| 57,5297042980419 | 13,0564098529644 | |||||
| 51,7636354053612 | 23,8162834731725 | |||||
| 48,8416044030217 | 25,6088846894081 | |||||
| 49,1023643158868 | 24,6671603771976 | |||||
| 55,2603213378133 | 15,386060383049 | |||||
| 47,528507932783 | 25,1045522734005 | |||||
| 48,6658256620266 | 25,7922292926967 | |||||
| 51,654341441262 | 21,9474698222543 | |||||
| 60,2570674752622 | 11,3550453521798 | |||||
| 52,7169346488304 | 22,5385497234589 | |||||
| 51,4747665002755 | 25,3675387405723 | |||||
| 53,6892534694114 | 23,1769672338028 | |||||
| 60,0874574778528 | 15,2997627075693 | |||||
| 50,540239086024 | 26,2299498216884 |
| Zadanie |
| Dokaonaj identyfikacji modelu ARMA (do p=3 i q=3) dla poniższego szeregu |
| Yt |
| 1,6934723 |
| 1,3040391 |
| 1,2957693 |
| 0,40598454 |
| 0,12425803 |
| -0,35923848 |
| -0,84672123 |
| -2,2353983 |
| -2,3881432 |
| -0,44474021 |
| -0,22861908 |
| -1,1653847 |
| 0,87295983 |
| 1,549451 |
| 0,0045300819 |
| 0,75730961 |
| -0,65756099 |
| 1,4759265 |
| 1,0316313 |
| 0,75066231 |
| 0,91297555 |
| -0,42199815 |
| 0,73816567 |
| 1,1714058 |
| -0,44137184 |
| -0,13920141 |
| -1,0838609 |
| -0,90986252 |
| -1,6920258 |
| -1,3892181 |
| -0,52497006 |
| 0,97455853 |
| 0,36998309 |
| -0,89579304 |
| -0,41085776 |
| -1,1657919 |
| -1,2285244 |
| 1,2487575 |
| 0,91634723 |
| -0,7391479 |
| -0,50455993 |
| -0,71880353 |
| -1,0394617 |
| -0,57293629 |
| -0,56069655 |
| -0,084474084 |
| 1,6517755 |
| 0,49361433 |
| -0,49978354 |
| 0,69691826 |
| 1,25749 |
| 1,0078869 |
| 0,33828185 |
| -1,1066812 |
| 0,11917161 |
| 0,069320637 |
| 0,028094573 |
| -0,39130732 |
| 0,21510975 |
| -0,045189908 |
| -0,70670025 |
| -1,7021921 |
| -1,7652484 |
| 1,2381812 |
| 2,991105 |
| 0,031365529 |
| -0,62335848 |
| 0,0068517728 |
| -0,40786049 |
| 1,6153633 |
| 1,4774454 |
| -0,33997687 |
| -1,5568899 |
| -0,52830623 |
| 0,11398371 |
| -1,3390133 |
| -0,011061902 |
| 0,39418065 |
| 1,3515234 |
| 0,42910833 |
| 0,39880045 |
| -0,39446867 |
| -0,31194829 |
| 1,2199685 |
| 2,0173667 |
| 0,79197521 |
| 2,5886134 |
| 1,1869116 |
| 1,2439476 |
| 0,8910753 |
| -0,20819459 |
| 1,6781688 |
| 1,2091766 |
| -0,12569695 |
| -0,31683863 |
| 0,23609192 |
| 0,15726379 |
| 0,061203814 |
| -0,13616016 |
| -1,0458975 |
| -0,50882911 |
| -1,5559672 |
| -0,92939618 |
| 0,011938302 |
| 0,38218234 |
| 1,087337 |
| -0,71195533 |
| -1,7987526 |
| 1,4096025 |
| 3,7122512 |
| 2,2676118 |
| -0,11028947 |
| 0,30571115 |
| 0,48775736 |
| -1,9712641 |
| -0,96491056 |
| -0,087767014 |
| 0,39285011 |
| 0,31896218 |
| -3,4566775 |
| -2,8829127 |
| -2,0335651 |
| -1,5263368 |
| -2,25344 |
| -1,1941915 |
| -1,0562377 |
| 0,12616291 |
| -0,40455238 |
| 0,23661362 |
| -1,0959297 |
| -2,6059402 |
| -1,9498709 |
| 0,11495432 |
| 1,4547454 |
| -0,037470351 |
| 1,2522591 |
| 0,65708236 |
| 0,061348921 |
| -0,22939718 |
| -0,7010939 |
| -0,016150798 |
| 0,70434304 |
| 0,079458575 |
| -2,7942833 |
| 0,81050041 |
| 0,12048303 |
| 1,4439509 |
| 1,9776301 |
| -2,1677575 |
| -1,3431805 |
| 0,24840296 |
| 0,91752415 |
| 0,98825638 |
| 0,87359224 |
| 0,57943692 |
| 0,55435587 |
| 1,8796285 |
| 1,3521435 |
| 0,080337556 |
| -0,07878021 |
| 0,63656413 |
| 0,27836157 |
| -0,81148038 |
| -1,4377638 |
| -0,22233395 |
| 1,1266389 |
| 1,7949593 |
| 1,5545227 |
| -0,2807447 |
| 0,45403418 |
| -0,59374536 |
| -0,62674417 |
| -1,4157555 |
| 0,65386369 |
| 1,1158787 |
| 1,1527837 |
| 0,33683976 |
| 0,24039565 |
| -0,9271278 |
| -1,8445615 |
| -1,6846627 |
| 1,2875536 |
| 1,2683868 |
| -0,13535423 |
| -0,66288293 |
| -1,3117772 |
| 0,77083395 |
| 1,630591 |
| 0,94268342 |
| 0,67212219 |
| 1,5195853 |
| 1,7819171 |
| 2,0285673 |
| -0,26952489 |
| -1,1386903 |
| 0,8849238 |
| 1,695147 |
| 1,6399814 |
| 0,68213947 |
| 0,32339625 |
| Yt | Xt | dane miesięczne | ||||
| 21,0445 | 31,0964 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 20,2426 | 29,4048 | Yt | - | |||
| 20,7079 | 30,0116 | Xt | 1 | 3 | ||
| 21,3447200207481 | 28,9102381405296 | |||||
| 21,6114869880588 | 29,0038610295878 | |||||
| 21,115889509644 | 30,0432641272327 | |||||
| 20,2181968193524 | 30,4079691571101 | |||||
| 20,3087048312362 | 30,3526885265183 | |||||
| 23,2277923784009 | 30,8684510375975 | |||||
| 21,9646104951291 | 30,275983349092 | |||||
| 22,5027800349099 | 30,5064876154307 | |||||
| 21,5474262943077 | 28,2204973664665 | |||||
| 20,9040173911156 | 29,4711480346908 | |||||
| 20,5007070873706 | 28,1297405076683 | |||||
| 22,5157336856658 | 30,3844892417149 | |||||
| 22,7866601653554 | 29,7005860903913 | |||||
| 24,9902715979917 | 29,9948503252156 | |||||
| 23,1393532847546 | 30,6782881739037 | |||||
| 21,4650438807563 | 33,0273107838287 | |||||
| 21,8161295220246 | 31,2377028574252 | |||||
| 23,222651245289 | 32,166157314823 | |||||
| 22,2698368817058 | 28,9411430893556 | |||||
| 21,2146503178039 | 29,0522924765752 | |||||
| 20,1227075497127 | 28,6198869497872 | |||||
| 20,6888929047363 | 29,2495912949738 | |||||
| 20,9124673090762 | 28,7046623666054 | |||||
| 23,2539232325921 | 30,4525974184979 | |||||
| 21,6014569847005 | 29,3437389020856 | |||||
| 23,6146914697671 | 30,2631900934797 | |||||
| 20,6943057862333 | 29,8767162430139 | |||||
| 21,3197006121753 | 30,7765389934351 | |||||
| 20,8197768208 | 30,8323002502693 | |||||
| 19,0693822957415 | 30,3996985995893 | |||||
| 22,6545549862041 | 32,1569014361474 | |||||
| 23,7162625057054 | 30,1797903915114 | |||||
| 23,1570368293601 | 32,8140049458332 | |||||
| 21,2854974398727 | 30,4109597977238 | |||||
| 22,4743140187163 | 29,970719284082 | |||||
| 21,4033265045467 | 27,7891185205997 | |||||
| 20,3253496318442 | 27,9107949380397 | |||||
| 20,7590795642971 | 28,8671686621873 | |||||
| 21,2798429425643 | 29,0571159746043 | |||||
| 23,511739124859 | 32,0487611958109 | |||||
| 22,8155014684227 | 31,1139577774304 | |||||
| 22,4001007168771 | 31,6232798302806 | |||||
| 21,5122600820414 | 31,4351029922353 | |||||
| 21,3151144827199 | 31,3523541889393 | |||||
| 21,9764757160191 | 33,498887444978 | |||||
| 23,6662557769593 | 31,7856181252216 | |||||
| 24,1964745503624 | 32,7453662708385 | |||||
| 23,5153925473819 | 30,9603277110739 | |||||
| 23,5779254720087 | 30,4044828828516 | |||||
| 22,9097536360945 | 31,4064147888654 | |||||
| 23,4423054429977 | 29,49612819596 | |||||
| 21,8009926772085 | 29,1258047776653 | |||||
| 21,4242944807327 | 28,9045383676141 | |||||
| 22,4531338628712 | 31,488738814676 | |||||
| 22,710812965817 | 31,8968438435568 | |||||
| 22,3450143239025 | 32,6009202770141 | |||||
| 24,0183435005663 | 33,5028575563403 | |||||
| 23,7221551143648 | 32,786121848197 | |||||
| 21,4242515723009 | 32,7656463204175 | |||||
| 22,3790057437178 | 31,1200528354415 | |||||
| 23,1572948826307 | 31,1630012277508 | |||||
| 22,2614867421826 | 32,0900873231994 | |||||
| 21,6649344670549 | 31,8323421951566 | |||||
| 23,6188957580267 | 33,4378312685036 | |||||
| 22,9443359306187 | 32,1978839550093 | |||||
| 21,30134672493 | 31,3487113145253 | |||||
| 21,2660066835824 | 31,5633257215172 | |||||
| 23,5126323522582 | 31,3466320362661 | |||||
| 24,7193607205071 | 32,2864346753098 | |||||
| 21,406133672571 | 33,9285852717622 | |||||
| 21,3843357901769 | 33,8740551583971 | |||||
| 22,0742756908512 | 34,049321741505 | |||||
| 23,845936394307 | 33,4846925380696 | |||||
| 22,9759659967104 | 34,1450010136139 | |||||
| 23,7898625904239 | 34,3282440212882 | |||||
| 23,6863560972721 | 33,4469082092432 | |||||
| 25,4313140838987 | 35,6977179292096 | |||||
| 25,6261773784514 | 33,6948544160411 | |||||
| 24,6034282869686 | 34,8929463865389 | |||||
| 23,7219064109235 | 33,6223805708937 | |||||
| 23,352838721693 | 35,1053413752897 | |||||
| 23,2188767186724 | 34,9120297191342 | |||||
| 24,0269394159917 | 36,9860441298887 | |||||
| 24,4106682801587 | 33,9475671186155 | |||||
| 26,827563213669 | 36,3622475663091 | |||||
| 23,9839436035159 | 36,1220098493924 | |||||
| 23,6878572780579 | 38,207966755805 | |||||
| 23,0768067867558 | 36,4075334950389 | |||||
| 22,8241187832039 | 36,7458081538864 | |||||
| 24,9421803800756 | 37,1605515896825 | |||||
| 24,9231678959935 | 36,6965667009676 | |||||
| 25,1590002312257 | 36,3170438667081 | |||||
| 25,1676433825407 | 37,5622860123786 | |||||
| 25,4578382543303 | 38,0745714272461 | |||||
| 25,373334103127 | 37,2036198867196 | |||||
| 26,285034632282 | 38,4234861577299 | |||||
| 23,3944995901451 | 37,3778633752046 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | wyrównać szereg czasowy za pomocą trendu pełzającego (k=3) |
| b) | wyznaczyć wartości prognoz za pomocą wag harmonicznych |
| c) | policzyć prognozy oraz błędy prognoz |
| yt | |
| 22,6 | |
| 24,5 | |
| 23,9 | |
| 26,9 | |
| 30,9 | |
| 32,8 | |
| 34,5 | |
| 38,2 | |
| 39,2 | |
| 39,8 | |
| 39,9 | |
| 39,3 | |
| 40,8 | |
| 41 | |
| 41,8 | |
| 40,5 | |
| 46,7 |
| Yt | Xt | dane kwartalne | ||||
| 38,1241 | 8,6060 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 37,3994 | 8,4806 | Yt | 3 | |||
| 36,9547 | 8,7032 | Xt | 0 | - | ||
| 37,6273532369218 | 9,78062476453626 | |||||
| 37,3196574491066 | 10,0099425762237 | |||||
| 39,3858780884037 | 9,09858385875095 | |||||
| 40,0776410940262 | 8,05500915650838 | |||||
| 41,5316561606029 | 8,1676294206289 | |||||
| 44,4486757985527 | 10,8804119633619 | |||||
| 43,1171909387389 | 9,8542171554923 | |||||
| 43,5127498570696 | 10,3001849887376 | |||||
| 42,3487875930005 | 10,2592273477211 | |||||
| 42,4599589622916 | 9,11555817723928 | |||||
| 41,9938898476572 | 9,24881088430331 | |||||
| 43,8057169338855 | 10,3619379889799 | |||||
| 45,5777532705076 | 10,9064257291989 | |||||
| 46,0953743663326 | 12,9923314679055 | |||||
| 44,5668507574949 | 10,8680380151931 | |||||
| 44,9387122494852 | 8,25411956722488 | |||||
| 44,4269326283357 | 9,32104837905452 | |||||
| 45,1736746940065 | 10,3561883193598 | |||||
| 46,5340996799065 | 10,6933796459635 | |||||
| 46,663990186971 | 9,59373332717383 | |||||
| 47,6223423436517 | 8,67475276979785 | |||||
| 47,5579165259164 | 8,98905638674678 | |||||
| 48,6985548421874 | 9,43060236243403 | |||||
| 50,0902822531731 | 11,072884265193 | |||||
| 49,0192818294893 | 9,86396142386628 | |||||
| 51,0452993281754 | 11,5094154323752 | |||||
| 48,9439294665056 | 8,74361928902774 | |||||
| 48,5422474763885 | 9,0090850148013 | |||||
| 47,2601983648572 | 8,48685672069233 | |||||
| 48,9392182583659 | 6,90950285590577 | |||||
| 49,5399944745902 | 9,79179441174519 | |||||
| 50,8502494605236 | 11,6443463491009 | |||||
| 50,3246575710901 | 10,0314348510269 | |||||
| 49,7552511148804 | 9,12111352078318 | |||||
| 50,0047031181717 | 10,4860263050835 | |||||
| 51,0797255206694 | 10,2876790963068 | |||||
| 51,2912183482357 | 9,16103165662835 | |||||
| 52,6248039066663 | 9,21221209942213 | |||||
| 53,2306552187832 | 9,65699655272256 | |||||
| 53,8366719882905 | 10,6922346465346 | |||||
| 55,6304944673658 | 10,3699183574506 | |||||
| 55,8734190756801 | 9,75078878476488 | |||||
| 54,3288040060463 | 8,93821888514728 | |||||
| 53,9265062699845 | 8,77417280714417 | |||||
| 54,084196080772 | 8,5769207380279 | |||||
| 55,5733174979227 | 10,9520085268707 | |||||
| 54,8596561080471 | 11,098328042027 | |||||
| 54,4718647050098 | 11,1312614629523 | |||||
| 55,0619454376337 | 11,416132318868 | |||||
| 54,0813175830394 | 10,3471877205483 | |||||
| 58,1250977484277 | 11,6438541646138 | |||||
| 56,1633047102498 | 10,1506707661424 | |||||
| 55,1360827295743 | 9,86247913368706 | |||||
| 55,9703605566414 | 9,85763833700082 | |||||
| 57,8703995704026 | 9,95207542839429 | |||||
| 57,23404973756 | 9,3046462130969 | |||||
| 57,1809797935054 | 10,6172004780302 | |||||
| 58,4209019461916 | 10,607706375086 | |||||
| 58,1016727294226 | 8,31799304413396 | |||||
| 60,1381078989615 | 9,93098460954118 | |||||
| 61,3890809275016 | 10,6920943915304 | |||||
| 59,2872567484122 | 9,42545181290285 | |||||
| 58,7017073694333 | 8,9319975889923 | |||||
| 57,8535597885628 | 10,2437632506253 | |||||
| 59,8828801244836 | 10,065182348615 | |||||
| 57,7515961182109 | 8,76186219911989 | |||||
| 60,5711689231726 | 8,64067639497546 | |||||
| 62,1562097666666 | 10,9739795377518 | |||||
| 62,0587977766781 | 11,8047868503832 | |||||
| 59,3747907194272 | 7,83469956386609 | |||||
| 58,8921996024522 | 7,83471372681807 | |||||
| 59,3780738026845 | 8,45454699424921 | |||||
| 59,2450349932121 | 10,4520593790792 | |||||
| 59,0410785866622 | 9,31796559126483 | |||||
| 61,4952472052948 | 10,0585649819087 | |||||
| 60,8101232883352 | 10,3075928135749 | |||||
| 62,8017996425656 | 11,1522269122148 | |||||
| 63,1325256432932 | 12,148235612035 | |||||
| 62,3397178904933 | 10,646249732353 | |||||
| 61,7587881359461 | 10,272954182566 | |||||
| 62,602946446189 | 9,31070217157711 | |||||
| 63,4629112768484 | 9,25406483101875 | |||||
| 64,8899037976156 | 9,23252176403624 | |||||
| 67,2902747801755 | 10,8316414327125 | |||||
| 69,0018813649055 | 12,2826641871454 | |||||
| 65,7272192889888 | 9,53513966375894 | |||||
| 65,9389842447812 | 8,40467057573586 | |||||
| 65,359538931881 | 8,51379338874025 | |||||
| 64,5825655046468 | 8,12579552164937 | |||||
| 67,933949968162 | 10,0779597442026 | |||||
| 67,3321194338738 | 10,2445412156065 | |||||
| 69,6753980035118 | 10,6321826845425 | |||||
| 70,3701259167857 | 10,1427289775893 | |||||
| 69,2140306418433 | 10,2280096834319 | |||||
| 67,8318076731917 | 10,4918861484392 | |||||
| 68,8978733094696 | 10,91564016919 | |||||
| 67,797657039867 | 8,44335424006326 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | 0,262 | y2t + | 0,078 | y1t-1 + | 0,158 | y2t-1 + | -0,433 | x1t + | -0,335 | x2t + | 0,191 | x3t |
| y2t | = | 0,296 | y1t + | 0,368 | y1t-1 + | 0,442 | y2t-1 + | 0,19 | x1t + | 0,48 | x2t + | -0,159 | x3t |
| Yt | Xt | dane kwartalne | ||||
| 53,5977 | 68,6462 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 53,3591 | 68,8497 | Yt | ||||
| 53,3382 | 69,6696 | Xt | 1 | - | 1 | |
| 54,9180017170754 | 71,3079765421383 | |||||
| 55,7506565969494 | 72,1845882710692 | |||||
| 58,7297200048835 | 72,2200941355346 | |||||
| 60,2616229015632 | 72,0187470677673 | |||||
| 60,1581297976031 | 72,5790735338836 | |||||
| 61,399610581928 | 75,5026367669418 | |||||
| 59,2123669304239 | 74,9156183834709 | |||||
| 60,0627643395833 | 76,6950091917355 | |||||
| 60,1684101260677 | 77,3129045958677 | |||||
| 61,4367172826785 | 76,9324522979339 | |||||
| 62,4110380125801 | 77,7350261489669 | |||||
| 64,0419226783008 | 79,1397130744835 | |||||
| 66,1199581610616 | 80,1699565372417 | |||||
| 66,5984373870643 | 83,1326782686209 | |||||
| 64,5434857793411 | 81,9101391343104 | |||||
| 66,3218755271235 | 80,6728695671552 | |||||
| 66,7248457754552 | 82,0908347835776 | |||||
| 66,0539184410718 | 82,8173173917888 | |||||
| 68,0109039031195 | 83,6202586958944 | |||||
| 69,1931480080306 | 83,3640293479472 | |||||
| 70,2204503705114 | 83,2679146739736 | |||||
| 69,5401962192147 | 83,9637573369868 | |||||
| 69,5379072867801 | 84,6203786684934 | |||||
| 71,3122856538275 | 86,7644893342467 | |||||
| 70,6854945633508 | 86,2389446671233 | |||||
| 73,5326666930064 | 89,0187723335617 | |||||
| 72,09082523986 | 86,7574861667808 | |||||
| 72,0372491807474 | 88,0688430833904 | |||||
| 70,7201524256032 | 87,5398215416952 | |||||
| 73,2449080731352 | 86,3387107708476 | |||||
| 75,0945452047094 | 89,5524553854238 | |||||
| 74,8211836759205 | 91,3975276927119 | |||||
| 75,2206141221996 | 90,9455638463559 | |||||
| 76,150595230641 | 91,471481923178 | |||||
| 76,7332414203036 | 93,370640961589 | |||||
| 77,9404761058235 | 93,4663204807945 | |||||
| 79,3046413078887 | 93,1961602403973 | |||||
| 80,6139257741595 | 93,9160801201986 | |||||
| 80,4870751692396 | 94,6572400600993 | |||||
| 80,3323911340456 | 96,1560200300496 | |||||
| 82,347328138757 | 96,4989100150248 | |||||
| 83,742221449822 | 96,8229550075124 | |||||
| 81,7628748625279 | 96,6852775037562 | |||||
| 80,8649423754183 | 96,9729387518781 | |||||
| 81,9236759935705 | 97,0577693759391 | |||||
| 84,6023113832264 | 99,8246846879695 | |||||
| 84,3822571397775 | 100,407742343985 | |||||
| 84,8965332290273 | 101,671571171992 | |||||
| 86,7435882966449 | 102,915785585996 | |||||
| 86,9306184621589 | 102,636392792998 | |||||
| 91,4594625779125 | 104,713296396499 | |||||
| 89,8077949062047 | 103,58954819825 | |||||
| 87,3116776464431 | 104,175074099125 | |||||
| 88,2420595116607 | 104,459137049562 | |||||
| 91,6484021604014 | 104,911568524781 | |||||
| 91,6208464880248 | 104,741684262391 | |||||
| 90,6441950676608 | 106,621342131195 | |||||
| 91,7244916472547 | 107,001171065598 | |||||
| 93,004857973565 | 105,599885532799 | |||||
| 95,4600978463691 | 107,954242766399 | |||||
| 95,7001692649201 | 108,6991213832 | |||||
| 93,2154403278403 | 108,2082606916 | |||||
| 92,8149780139921 | 108,6310303458 | |||||
| 93,3913772238943 | 110,3209151729 | |||||
| 96,6947532237472 | 110,48335758645 | |||||
| 96,7346625533743 | 110,044078793225 | |||||
| 98,9685515910176 | 110,601339396613 | |||||
| 100,76217563894 | 113,182869698306 | |||||
| 99,2288455841395 | 114,401434849153 | |||||
| 96,908314289966 | 111,625217424577 | |||||
| 98,1694830876426 | 112,771408712288 | |||||
| 99,2030561045245 | 113,073304356144 | |||||
| 99,8141278676906 | 115,211852178072 | |||||
| 100,137662980364 | 114,634226089036 | |||||
| 104,465269896574 | 116,552313044518 | |||||
| 104,253893214154 | 117,349856522259 | |||||
| 105,340195030627 | 118,99092826113 | |||||
| 106,273049105452 | 120,759864130565 | |||||
| 105,747365296403 | 120,197732065282 | |||||
| 106,28796553272 | 120,893166032641 | |||||
| 107,700191488052 | 120,314683016321 | |||||
| 109,299058695403 | 120,63794150816 | |||||
| 110,090463924989 | 120,81767075408 | |||||
| 111,840290986044 | 122,80043537704 | |||||
| 112,870414978592 | 124,73681768852 | |||||
| 109,498271519775 | 123,01170884426 | |||||
| 110,334533786995 | 123,12775442213 | |||||
| 111,206017900281 | 123,335877211065 | |||||
| 110,676327444046 | 122,958238605532 | |||||
| 114,686694265043 | 125,248319302766 | |||||
| 114,902577115074 | 125,767459651383 | |||||
| 116,879281328115 | 127,217029825692 | |||||
| 118,236380610442 | 127,608514912846 | |||||
| 116,714360159458 | 128,550557456423 | |||||
| 114,886885999142 | 129,395978728211 | |||||
| 117,387485201465 | 130,436089364106 | |||||
| 118,821386774293 | 128,651144682053 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | 0,437 | y2t + | 0,237 | y1t-1 + | -0,429 | y2t-1 + | 0,467 | y3t-1 + | -0,183 | x1t + | -0,268 | x2t |
| y2t | = | 0,217 | y3t + | 0,274 | y1t-1 + | 0,273 | y2t-1 + | -0,467 | y3t-1 + | -0,367 | x1t + | -0,353 | x2t |
| y3t | = | 0,025 | y1t + | -0,045 | y1t-1 + | -0,475 | y2t-1 + | -0,449 | y3t-1 + | 0,254 | x1t + | -0,466 | x2t |
| Yt | Xt | dane miesięczne | ||||
| 122,0364 | 130,2822 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 120,2440 | 131,4344 | Yt | 2 | - | 2 | |
| 121,2683 | 133,3275 | Xt | ||||
| 121,592683975763 | 132,260854521314 | |||||
| 123,666618953704 | 133,319927260657 | |||||
| 126,616569126764 | 135,581163630329 | |||||
| 125,578567531991 | 135,153881815164 | |||||
| 126,831251984057 | 134,888340907582 | |||||
| 127,995838557228 | 137,405970453791 | |||||
| 125,753185787029 | 136,672185226896 | |||||
| 127,845860423325 | 139,125992613448 | |||||
| 129,008050879164 | 137,834296306724 | |||||
| 130,858237894909 | 137,983148153362 | |||||
| 132,772378399183 | 138,532874076681 | |||||
| 131,46015883367 | 139,35543703834 | |||||
| 129,831663379999 | 140,28291851917 | |||||
| 132,762014610583 | 143,666759259585 | |||||
| 133,633165764434 | 142,636279629793 | |||||
| 134,698733635384 | 142,226139814896 | |||||
| 135,255575961251 | 140,973169907448 | |||||
| 135,369895079851 | 141,677784953724 | |||||
| 135,499093851959 | 141,619692476862 | |||||
| 134,863340504713 | 142,708046238431 | |||||
| 137,511858232657 | 145,033323119216 | |||||
| 136,798422271045 | 145,698461559608 | |||||
| 139,186358151704 | 146,820430779804 | |||||
| 139,804160725293 | 148,502615389902 | |||||
| 140,159683710782 | 148,053507694951 | |||||
| 142,98282553931 | 149,039553847475 | |||||
| 145,089939009144 | 149,271676923738 | |||||
| 145,016287398647 | 150,427338461869 | |||||
| 143,74207772938 | 151,028769230934 | |||||
| 142,4452965281 | 150,651184615467 | |||||
| 145,949636016414 | 153,593892307734 | |||||
| 148,797673369498 | 153,221446153867 | |||||
| 149,118824336707 | 151,008723076933 | |||||
| 149,128751380208 | 150,989461538467 | |||||
| 149,512364077619 | 152,329630769233 | |||||
| 148,983925225328 | 153,405615384617 | |||||
| 149,741342488221 | 153,916907692308 | |||||
| 153,706254882393 | 156,111753846154 | |||||
| 151,393210037771 | 155,735076923077 | |||||
| 153,535975381175 | 156,905938461539 | |||||
| 153,90889890556 | 157,285469230769 | |||||
| 153,309996158345 | 156,979234615385 | |||||
| 153,033046287079 | 155,923117307692 | |||||
| 155,176663206848 | 157,329258653846 | |||||
| 156,683352364577 | 157,647929326923 | |||||
| 156,655773689773 | 157,309964663462 | |||||
| 156,618655795664 | 159,816082331731 | |||||
| 156,340358160382 | 160,241041165865 | |||||
| 158,008455683666 | 161,013620582933 | |||||
| 160,744180359245 | 160,969310291466 | |||||
| 162,086664300421 | 161,883155145733 | |||||
| 161,028448027805 | 160,493977572867 | |||||
| 162,401294479899 | 161,456988786433 | |||||
| 163,775942215109 | 162,115194393217 | |||||
| 163,520691403768 | 163,602597196608 | |||||
| 165,317947919169 | 165,150498598304 | |||||
| 166,783914393199 | 165,417549299152 | |||||
| 167,537313613215 | 166,104774649576 | |||||
| 169,438919124793 | 168,135787324788 | |||||
| 170,47293461848 | 170,190493662394 | |||||
| 169,809487921224 | 169,772946831197 | |||||
| 170,891823366568 | 170,527073415599 | |||||
| 173,015586022659 | 170,745036707799 | |||||
| 174,24017628651 | 169,6834183539 | |||||
| 174,360440700131 | 171,43470917695 | |||||
| 175,156405829807 | 172,625154588475 | |||||
| 175,301034727972 | 173,872677294237 | |||||
| 177,053550441237 | 176,034838647119 | |||||
| 178,038683649467 | 175,905419323559 | |||||
| 178,430884494027 | 176,12050966178 | |||||
| 179,93709174398 | 175,90545483089 | |||||
| 179,674529452149 | 177,881627415445 | |||||
| 179,315983433399 | 177,173713707722 | |||||
| 180,249262379763 | 177,612656853861 | |||||
| 182,084818171096 | 179,345528426931 | |||||
| 181,968267707173 | 178,516364213465 | |||||
| 182,369037096238 | 177,893982106733 | |||||
| 186,204103369325 | 179,161691053366 | |||||
| 187,021745762446 | 180,190945526683 | |||||
| 184,790051807189 | 178,539272763342 | |||||
| 184,542844520657 | 180,215036381671 | |||||
| 186,430111721886 | 182,392718190835 | |||||
| 190,102610037208 | 184,357959095418 | |||||
| 191,535129157367 | 184,029279547709 | |||||
| 190,898545805311 | 184,600139773854 | |||||
| 191,20602910579 | 184,474369886927 | |||||
| 195,350959404438 | 185,827284943464 | |||||
| 196,145163617045 | 185,650542471732 | |||||
| 197,332714608284 | 187,012671235866 | |||||
| 196,112922698044 | 187,317535617933 | |||||
| 196,365413004849 | 187,422767808966 | |||||
| 196,424442503943 | 186,844083904483 | |||||
| 197,927487790703 | 187,733641952242 | |||||
| 199,374008071857 | 186,667420976121 | |||||
| 199,897081343989 | 189,09781048806 | |||||
| 199,630888117035 | 189,83610524403 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 17,7 | |
| 18,6 | |
| 18,8 | |
| 19,65 | |
| 19,4 | |
| 18,8 | |
| 18,55 | |
| 18,95 | |
| 19,5 | |
| 20,9 | |
| 22 | |
| 22 | |
| 21,7 | |
| 22 | |
| 20,3 | |
| 19,75 | |
| 20,8 | |
| 21,2 | |
| 21,2 | |
| 18,8 | |
| 18,55 | |
| 18 | |
| 18,65 | |
| 19,15 | |
| 18,8 | |
| 18,75 | |
| 19,4 | |
| 19,35 | |
| 19,85 | |
| 19,95 | |
| 21,2 | |
| 22,1 | |
| 21,7 | |
| 21,9 | |
| 23 | |
| 22,3 | |
| 22,1 | |
| 22,2 | |
| 22,5 | |
| 23,1 | |
| 23,8 | |
| 25,8 | |
| 25,1 | |
| 25,3 | |
| 23,7 | |
| 21,5 | |
| 23,5 | |
| 24,6 | |
| 23,9 | |
| 24,4 |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | 1 | + | 3 | |
| 12,3805 | 25,9273 | Xt | ||||
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | ||||
| Wiedząc, że dla poniższych danych (z pominięciem ostatnich dwóch obserwacji) pominięciemzachodzi zależność | ||||
| Y1t=f1(stała, Y2t, Y1,t-1, X1,t-1) | ||||
| Y2t=f2(stała, Y1t, X2t) | ||||
| Korzystając z symulacji wyznaczyć mnożniki bezpośrenie i pośrednie oraz podać interpretacje | ||||
| zaburzenie w 1980 roku (wartość zmiennej zaburzonej jest o 1% wieksza od wartości pierwotnej) | ||||
| t | Y1t | Y2t | X1t | X2t |
| 1945 | 6509198,48 | 6474855,36 | 0,742 | 3682771 |
| 1946 | 6339875,00496 | 6341607,889 | 0,807730426165 | 3372076 |
| 1947 | 6953428,1457 | 6926832,09882 | 0,644349516394 | 3873411 |
| 1948 | 6600331,46847 | 6414101,86325 | 0,82472950017 | 3946958 |
| 1949 | 7634026,84837 | 7271796,75194 | 0,76847716593 | 4697254 |
| 1950 | 7306971,87537 | 7159651,92818 | 0,749848537983 | 4610003 |
| 1951 | 6935406,25422 | 7068456,90156 | 0,810677074964 | 4760705 |
| 1952 | 7061308,69756 | 7241027,30883 | 0,815996411571 | 4679684 |
| 1953 | 7034487,62036 | 7050294,56867 | 0,783204476569 | 4374679 |
| 1954 | 7073328,74343 | 6990649,88967 | 0,783589199064 | 4284740 |
| 1955 | 6286323,74365 | 6731237,79492 | 0,794555187683 | 3656541 |
| 1956 | 6063944,42719 | 6393813,83286 | 0,807966303542 | 3800250 |
| 1957 | 6519698,0999 | 6470789,21674 | 0,80062399568 | 3816152 |
| 1958 | 5890150,08824 | 6384963,24416 | 0,80446891118 | 3375579 |
| 1959 | 6721662,92166 | 6896814,7976 | 0,768115157688 | 4039112 |
| 1960 | 6493092,57772 | 6609261,94415 | 0,712501525132 | 4220708 |
| 1961 | 6982293,79833 | 6744356,17306 | 0,682980965396 | 5091885 |
| 1962 | 6842215,82456 | 6639142,07121 | 0,673677497317 | 5170697 |
| 1963 | 6988981,66464 | 6805758,69507 | 0,665687426888 | 5213613 |
| 1964 | 6868563,89728 | 6766117,49528 | 0,670430678267 | 4830838 |
| 1965 | 6276943,81109 | 6254636,54304 | 0,685727966964 | 4477061 |
| 1966 | 6621595,13466 | 6586143,2531 | 0,707485878838 | 4307498 |
| 1967 | 6222740,97818 | 6158964,08652 | 0,719464878452 | 4029253 |
| 1968 | 6068632,80452 | 5800068,02347 | 0,746967010062 | 4078010 |
| 1969 | 6461289,78391 | 6443744,38285 | 0,732964428904 | 4183083 |
| 1970 | 6088310,79024 | 6485737,1911 | 0,725062236396 | 3865410 |
| 1971 | 8367297,55522 | 8175238,8266 | 0,723615006384 | 4405464 |
| 1972 | 6981261,03108 | 7227665,89382 | 0,692424742747 | 4571120 |
| 1973 | 7661561,7858 | 7770823,10773 | 0,662599728842 | 5625186 |
| 1974 | 7398131,0931 | 7303556,04591 | 0,638399637127 | 5469644 |
| 1975 | 7615026,69248 | 7675950,76977 | 0,632608970379 | 5560707 |
| 1976 | 7337132,27949 | 7341841,57474 | 0,636053053104 | 5143591 |
| 1977 | 6850299,37186 | 6856237,55269 | 0,662975628632 | 4866015 |
| 1978 | 6666779,6971 | 6693060,87266 | 0,634948103302 | 4641908 |
| 1979 | 6077734,90826 | 6167936,84623 | 0,671543160086 | 4034080 |
| 1980 | 6151785,63012 | 5325238,98163 | 0,581961502669 | 4192383 |
| 1981 | 6413475,62371 | 6702529,84052 | 0,744232898991 | 4366639 |
| 1982 | 5900684,53105 | 5988147,64222 | 0,663957489566 | 4073096 |
| 1983 | 6750391,63685 | 6658125,18344 | 0,636134191705 | 4737737 |
| 1984 | 6523781,29053 | 6439498,49835 | 0,611746149009 | 4396623 |
| 1985 | 6814154,31811 | 6743335,02724 | 0,609078651266 | 5010867 |
| 1986 | 6383933,74491 | 6395161,37375 | 0,615028675427 | 4686087 |
| 1987 | 7274048,81343 | 6499463,82555 | 0,609455995678 | 4690306 |
| 1988 | 5898660,47846 | 5851134,8492 | 0,614595268227 | 4459734 |
| 1989 | 5626432,81348 | 5639227,10813 | 0,632070958935 | 4081197 |
| 1990 | 6008598,32091 | 5666399,65378 | 0,645162341131 | 3870941 |
| 1991 | 5337588,71212 | 5393175,8508 | 0,689241030335 | 3597116 |
| 1992 | 5854002,80708 | 6009275,91272 | 0,704642502168 | 3853923 |
| 1993 | 5983520,66474 | 6060862,38064 | 0,709750595675 | 4043266 |
| 1994 | 5648007,76522 | 5860964,99577 | 0,711677396329 | 3835997 |
| 1995 | 6248845,75048 | 6455894,14309 | 0,721812555636 | 4262760 |
| 1996 | 6115163,66588 | 6572079,62051 | 0,728250358326 | 4280504 |
| 1997 | 6586995,54621 | 6488150,37236 | 0,701250079203 | 4820718 |
| 1998 | 6602481,23896 | 6449379,69735 | 0,708639199131 | 4707966 |
| 1999 | 6748075,63643 | 6647158,72696 | 0,728981539973 | 4770630 |
| 2000 | 7288913,81447 | 6250152,61535 | 0,708769191001 | 4485846 |
| 2001 | 6112494,63519 | 5924173,81666 | 0,723738705019 | 4122820 |
| 2002 | 6078912,19481 | 6165449,36443 | 0,762740390135 | 3983241 |
| 2003 | 5460132,61068 | 5658751,04867 | 0,786710938937 | 3589462 |
| 2004 | 5885756,22934 | 6433215,97706 | 0,840068394861 | 3850665 |
| Yt | Xt | dane miesięczne | ||||
| 70,8821 | 9,3599 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 69,8091 | 9,5896 | Yt | 1 | - | 3 | |
| 71,4759 | 11,0971 | Xt | ||||
| 70,2756603520336 | 9,46877743008091 | |||||
| 70,9804777949198 | 9,49474658709709 | |||||
| 73,3716403008317 | 11,4279400645243 | |||||
| 72,3577931432486 | 10,528846056133 | |||||
| 73,6308229787744 | 9,14744100870922 | |||||
| 74,1574004921885 | 11,0768666875147 | |||||
| 72,7848604974632 | 10,1634010411446 | |||||
| 73,7909694868288 | 11,6485405143179 | |||||
| 73,3907039185483 | 9,84654994481556 | |||||
| 73,8094836270124 | 8,99471281811242 | |||||
| 75,9466507177536 | 9,28469142561154 | |||||
| 75,4501406159029 | 9,93293186737204 | |||||
| 74,9575158554025 | 10,3862585060026 | |||||
| 76,7972323644509 | 13,0385496927897 | |||||
| 75,5580042204762 | 11,2062972945941 | |||||
| 74,6917731912137 | 9,29958373946013 | |||||
| 74,7513763968389 | 7,54800268135185 | |||||
| 75,2668706663367 | 8,27532621883788 | |||||
| 76,511962673964 | 8,45406230501339 | |||||
| 75,6682144330835 | 9,14263328685533 | |||||
| 78,1945456144522 | 10,9143979519236 | |||||
| 75,7487607542021 | 10,7962089899052 | |||||
| 77,3207455874256 | 10,6949851093755 | |||||
| 75,7242310367646 | 11,5010298577162 | |||||
| 75,8774045836912 | 10,3442193960454 | |||||
| 76,8840380617535 | 10,4346007407079 | |||||
| 78,671659741024 | 10,2659345515403 | |||||
| 78,948569887638 | 10,8940870535578 | |||||
| 78,7821386358572 | 10,9823631613168 | |||||
| 77,0086794953237 | 9,85975546459107 | |||||
| 79,1408271546584 | 12,1034687839005 | |||||
| 80,2867530473966 | 11,4183077525729 | |||||
| 79,5199851709547 | 8,07611324111632 | |||||
| 80,2751606228648 | 7,39766429478628 | |||||
| 82,4540099006337 | 9,11089817505825 | |||||
| 82,91972918855 | 10,2769497990932 | |||||
| 83,4088740734747 | 10,0193054470291 | |||||
| 85,8159426941755 | 11,1798677837866 | |||||
| 82,6216994646459 | 10,0633422577846 | |||||
| 84,9017679961137 | 10,2161107937563 | |||||
| 83,462431128173 | 10,1215527195428 | |||||
| 82,8688262976023 | 9,2324431216445 | |||||
| 81,4679654794384 | 7,61325574495942 | |||||
| 82,7931629646039 | 8,70459493598636 | |||||
| 83,782079792643 | 9,05162074450535 | |||||
| 83,4153106752929 | 8,10043189145677 | |||||
| 83,3482809311191 | 9,89582972237678 | |||||
| 82,9407032445288 | 9,95078529375136 | |||||
| 82,5865864557278 | 9,69974373016265 | |||||
| 83,5049375216787 | 8,82713627695592 | |||||
| 83,7950600486707 | 9,10214501942916 | |||||
| 83,4372525826087 | 7,35533162662781 | |||||
| 84,8592590609773 | 7,75702230748516 | |||||
| 86,480113004221 | 8,35861166575424 | |||||
| 86,3289977301047 | 9,39719914063157 | |||||
| 88,1911788438869 | 10,2402160705895 | |||||
| 88,1181636531658 | 9,54324829310529 | |||||
| 88,1506310333673 | 9,19555932537579 | |||||
| 89,7749227117552 | 10,6182051747563 | |||||
| 90,4348935975167 | 12,1730347897654 | |||||
| 89,1580733867026 | 10,7787558424558 | |||||
| 88,7560032024163 | 10,2780674842983 | |||||
| 89,7055135071328 | 9,9869069894124 | |||||
| 90,0991462343982 | 8,52093324941671 | |||||
| 90,4471536330655 | 9,85739452788464 | |||||
| 92,2964484918976 | 10,9802172891173 | |||||
| 91,5490953200987 | 11,4929902861933 | |||||
| 92,5089458774328 | 12,6509299563614 | |||||
| 91,6779453182377 | 11,5655678923227 | |||||
| 90,5917349754466 | 10,6553049592529 | |||||
| 91,366897887617 | 9,90318211192965 | |||||
| 90,3731958766871 | 11,5838995681889 | |||||
| 90,3819497526153 | 10,6538951505156 | |||||
| 89,216266368272 | 10,1775777048011 | |||||
| 90,1270213058954 | 11,4318203072459 | |||||
| 88,9319327161266 | 10,2062368421826 | |||||
| 88,3268892111261 | 8,70937232891754 | |||||
| 91,4460112446965 | 9,60751511180399 | |||||
| 92,1926427555077 | 10,6010458572267 | |||||
| 91,0932448191181 | 8,36206839507217 | |||||
| 90,5950652314029 | 9,14612044036807 | |||||
| 92,1270513890459 | 11,2496397016624 | |||||
| 93,9449960100521 | 12,6425837187208 | |||||
| 93,6130560438021 | 11,0966999488617 | |||||
| 92,3006041593973 | 10,3410748588146 | |||||
| 92,8872477845733 | 9,7158274447488 | |||||
| 96,1757841981337 | 10,74569126473 | |||||
| 96,6871386185635 | 10,2949973989404 | |||||
| 98,8599886107465 | 10,9111913200512 | |||||
| 98,1460478581649 | 10,6782964403435 | |||||
| 98,6633401400088 | 10,0297908241564 | |||||
| 97,4881562977873 | 8,84410647997515 | |||||
| 98,3330963271267 | 9,32471599274066 | |||||
| 99,0233520451317 | 8,10972605237778 | |||||
| 99,0197466130853 | 10,0215482283667 | |||||
| 99,4581075222876 | 10,56505629847 |
| Zadanie |
| Dokaonaj identyfikacji modelu ARMA (do p=3 i q=3) dla poniższego szeregu |
| Yt |
| -0,071539489 |
| 0,32927606 |
| 1,1427821 |
| -0,62010644 |
| -0,10794205 |
| 1,70975 |
| -0,37160986 |
| 0,49088804 |
| 0,32801232 |
| -0,7376865 |
| 1,3727321 |
| -0,69240905 |
| 1,1096615 |
| -1,824101 |
| 2,8125411 |
| -1,534353 |
| -0,84308874 |
| 1,0601016 |
| 0,53227998 |
| 0,26594646 |
| 1,19462 |
| 0,48360889 |
| -1,2479555 |
| -1,4320362 |
| 2,7911556 |
| -1,5630111 |
| 1,1144315 |
| -1,186079 |
| -0,70463923 |
| 0,71462056 |
| -1,874713 |
| 0,4730136 |
| -0,53975208 |
| 1,1337395 |
| -0,41788317 |
| -1,0528947 |
| 2,2189026 |
| -1,5204957 |
| 2,9347998 |
| -3,2633504 |
| 1,5017134 |
| -1,8184979 |
| 1,1657484 |
| -1,7930806 |
| 0,29116828 |
| -2,5829902 |
| 0,96990519 |
| -0,421588 |
| 0,1112776 |
| -0,24550962 |
| 0,054867822 |
| 0,1300807 |
| -0,59226279 |
| -0,29049247 |
| 0,71150942 |
| -0,91897813 |
| 0,87241806 |
| -1,5701897 |
| 0,95309018 |
| 0,077374901 |
| -0,94465846 |
| 0,80032278 |
| -0,79637025 |
| 0,48200004 |
| -0,69597194 |
| -1,5904545 |
| 0,96977244 |
| 0,71450077 |
| 0,15165355 |
| -0,48329104 |
| -0,32313933 |
| 0,47515551 |
| -0,71612501 |
| -0,027192296 |
| 0,074422971 |
| 1,2016725 |
| -3,3611744 |
| 2,9376782 |
| -3,0644391 |
| 3,0893922 |
| -4,5865317 |
| 2,9867408 |
| -2,0326486 |
| 0,99824004 |
| -0,90168597 |
| -0,8818968 |
| -0,5090241 |
| -0,45868529 |
| 0,68769397 |
| -1,0674925 |
| 2,2846538 |
| -1,4591861 |
| -0,84133637 |
| 0,13474236 |
| -0,74639376 |
| 0,62579351 |
| -0,65868708 |
| 0,18203759 |
| -0,86108832 |
| 0,53822825 |
| -1,8207638 |
| 1,886875 |
| -2,6443154 |
| 1,1894441 |
| -0,9787254 |
| 0,93319274 |
| -0,72986747 |
| 2,2490772 |
| 0,047617858 |
| 0,5931034 |
| -0,32335879 |
| -0,5812559 |
| -0,054457967 |
| -1,3678486 |
| 0,5829644 |
| -0,87898632 |
| 2,366586 |
| -0,90338562 |
| 0,69735927 |
| -0,78091575 |
| 0,62946387 |
| 0,32556677 |
| 2,0089531 |
| -1,0793805 |
| 1,6188703 |
| -0,45382259 |
| 0,87243344 |
| 0,39092702 |
| 0,98571623 |
| -0,6458503 |
| 0,13795753 |
| 0,13013737 |
| 0,90559578 |
| 0,58199468 |
| -0,95009869 |
| 1,5772974 |
| -1,2762493 |
| 0,55741989 |
| 0,15129285 |
| 0,82620622 |
| -1,148597 |
| -0,69458748 |
| 0,43586559 |
| 0,24791886 |
| -0,090045315 |
| 1,6405552 |
| -1,4791629 |
| 1,8305688 |
| -2,0661983 |
| 0,18321735 |
| 0,53840284 |
| -1,7695142 |
| -0,061902529 |
| -0,56169039 |
| -1,0953812 |
| 1,3253098 |
| -1,2050712 |
| -0,45013494 |
| -0,57334072 |
| -0,58518157 |
| 0,33800946 |
| -2,6511976 |
| 1,1614893 |
| -2,2044315 |
| 1,8727499 |
| -0,71238042 |
| 0,64584169 |
| -0,55352817 |
| -2,2475111 |
| 1,6013112 |
| -1,997228 |
| 1,1325821 |
| -1,1203854 |
| -0,37397771 |
| 0,84183761 |
| -0,3495306 |
| -0,1062135 |
| 0,96644793 |
| 0,90178528 |
| -1,7394236 |
| 1,1916655 |
| -1,9447936 |
| 2,1121897 |
| -0,97836574 |
| 0,16759513 |
| -0,67652608 |
| -0,27980236 |
| 1,1216743 |
| -1,0336924 |
| 0,57375014 |
| -1,6600405 |
| 1,4746482 |
| 1,6580232 |
| -0,87091994 |
| -0,81315905 |
| 0,81599705 |
| -2,0069708 |
| 1,5534527 |
| -2,7804895 |
| 2,6655311 |
| Yt | Xt | dane kwartalne | ||||
| 100,8243 | 11,4505 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 100,3592 | 10,2005 | Yt | ||||
| 100,6145 | 9,8259 | Xt | 0 | - | 2 | |
| 101,873075672962 | 10,5031070888171 | |||||
| 99,5534090598173 | 9,2164858843035 | |||||
| 100,301886784108 | 9,81111081550662 | |||||
| 98,6782137390841 | 10,8675096424623 | |||||
| 99,9775339719727 | 9,82372157657914 | |||||
| 99,1977209889003 | 9,96500789555089 | |||||
| 101,96451931841 | 10,4556874748017 | |||||
| 103,19250448328 | 11,7256413687356 | |||||
| 104,290757310376 | 10,8982144419273 | |||||
| 102,992094448299 | 9,45161481034297 | |||||
| 105,269776062831 | 10,6134430725933 | |||||
| 105,813089887759 | 10,4776370931938 | |||||
| 106,232217640533 | 10,7916856248189 | |||||
| 105,755942565681 | 11,7719516844513 | |||||
| 102,810715105385 | 9,17607015477999 | |||||
| 103,662236273703 | 8,2873495720546 | |||||
| 101,951656240799 | 7,7769537395933 | |||||
| 105,831346707457 | 9,48337199818027 | |||||
| 105,714688602432 | 10,2563998772121 | |||||
| 107,169496087277 | 11,455588339152 | |||||
| 106,066176264167 | 10,2435742064124 | |||||
| 106,263302982082 | 8,60671060146058 | |||||
| 105,815957465836 | 8,80678303880658 | |||||
| 106,747578178727 | 9,03397833896512 | |||||
| 107,520975008894 | 11,9622542578406 | |||||
| 106,585357593647 | 9,82883362723076 | |||||
| 105,775560653825 | 8,7675405362632 | |||||
| 107,633284531577 | 9,05802017996238 | |||||
| 108,075462706909 | 9,83834792910223 | |||||
| 109,002535612963 | 10,2633679105624 | |||||
| 109,628042022324 | 8,61237957655053 | |||||
| 110,218938605055 | 8,05177941510655 | |||||
| 110,796675474856 | 8,34487583458811 | |||||
| 111,359219178981 | 9,51500409276209 | |||||
| 110,812149041333 | 10,3694392960046 | |||||
| 110,635114384098 | 8,41581842017368 | |||||
| 110,210332435313 | 7,40997742128546 | |||||
| 111,15717813767 | 9,56204318459062 | |||||
| 112,612789566185 | 9,89152836590968 | |||||
| 112,081434380792 | 8,47925122757765 | |||||
| 112,586904269176 | 9,98866710401592 | |||||
| 114,264790450506 | 9,25065818373467 | |||||
| 115,2225405624 | 10,5169289606626 | |||||
| 116,596691577898 | 10,1509670252109 | |||||
| 115,741174781862 | 8,93060482440667 | |||||
| 113,51976093668 | 7,53981230464007 | |||||
| 116,252414409284 | 9,19752470499803 | |||||
| 116,046913459899 | 10,445418661107 | |||||
| 116,803026291374 | 10,2312519190541 | |||||
| 117,199931912442 | 10,0906003611949 | |||||
| 118,218926290127 | 10,1059246048812 | |||||
| 117,532936390829 | 10,2133821940821 | |||||
| 117,006699187475 | 8,7088137155767 | |||||
| 116,927300093444 | 8,32059219956371 | |||||
| 118,259141382178 | 10,2392519851088 | |||||
| 119,265449076512 | 12,4967483326853 | |||||
| 119,74300905714 | 12,57539857081 | |||||
| 119,39958796479 | 10,3167747855994 | |||||
| 118,723333374044 | 9,1861678215567 | |||||
| 121,169984834784 | 10,9899514750985 | |||||
| 119,54292658202 | 8,93182539108225 | |||||
| 122,230805703766 | 10,0239272530116 | |||||
| 120,718351727123 | 10,2923160091811 | |||||
| 118,692904470913 | 8,52557982868708 | |||||
| 119,172533422572 | 9,89489511158921 | |||||
| 120,856999789264 | 8,76867360718848 | |||||
| 119,509859909216 | 7,72196827011748 | |||||
| 120,290522031503 | 8,1531820529022 | |||||
| 120,879035581115 | 8,48410054541585 | |||||
| 119,538694553627 | 8,45869565683727 | |||||
| 119,841818321948 | 10,3317176647939 | |||||
| 121,628585502644 | 11,1521501353458 | |||||
| 122,133341391505 | 9,84345976823472 | |||||
| 119,93270400913 | 8,44008484351363 | |||||
| 123,415704161512 | 9,0887044912864 | |||||
| 123,450425941993 | 9,49612679258911 | |||||
| 125,280966846812 | 12,0394520489086 | |||||
| 124,653205832109 | 10,1944879866776 | |||||
| 125,517088520408 | 9,9828083786662 | |||||
| 125,345675503985 | 10,0940577933298 | |||||
| 124,969718950519 | 11,0835863830651 | |||||
| 124,307965018663 | 9,36627585353358 | |||||
| 124,042879288107 | 9,89126201184727 | |||||
| 125,748200770656 | 11,4422482498636 | |||||
| 123,538535141697 | 9,9914455213776 | |||||
| 124,828489016486 | 10,1300482857297 | |||||
| 123,203243575918 | 9,65699048645159 | |||||
| 124,743273604633 | 9,98728075750687 | |||||
| 125,648798242363 | 10,657943232818 | |||||
| 122,903250833216 | 7,83128738915692 | |||||
| 123,880983248819 | 8,00586072473307 | |||||
| 126,914074723351 | 9,98514414561946 | |||||
| 127,746005664056 | 9,52011385538981 | |||||
| 129,397263752629 | 9,86621368400907 | |||||
| 131,706773826748 | 9,25607268538759 | |||||
| 131,331985688218 | 8,56647223749108 |
| Zadanie |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich dwóch obserwacji) |
| dokonać wyrównania wykładniczego |
| oraz wyrównać szereg za pomocą sredniej 3-wyrazowj. |
| Obliczyć prognozy. Która metoda dała lepsze wyniki? |
| Pt |
| 36,1 |
| 37,4 |
| 38,6 |
| 37,6 |
| 38,1 |
| 37,8 |
| 39,9 |
| 40,2 |
| 40,8 |
| 42,5 |
| 45,5 |
| 46,4 |
| 46,2 |
| 44,1 |
| 45,8 |
| 48,3 |
| 49,8 |
| 50,3 |
| 50,2 |
| 54,2 |
| 55,6 |
| 58,5 |
| 60 |
| 64,3 |
| 68,2 |
| 67,7 |
| 69,8 |
| 81,4 |
| 72,2 |
| 72,3 |
| 72,2 |
| 74,5 |
| 72,9 |
| 69,6 |
| 71,5 |
| 73,4 |
| 80,5 |
| 89,4 |
| 96,3 |
| 102 |
| 116,5 |
| 115 |
| 129 |
| 110,5 |
| 100,5 |
| 98,1 |
| 96,2 |
| 82,5 |
| 88,5 |
| 99,5 |
| Yt | Xt |
| 48,1183107138122 | 64,1442 |
| 44,6353997167258 | 65,9714 |
| 39,0506105076807 | 67,1621 |
| 33,4033278345713 | 68,190702584866 |
| 51,9950409479241 | 69,6209053537098 |
| 48,9929799569888 | 72,7457716429085 |
| 43,4407589077525 | 76,0440236799703 |
| 37,2680251252945 | 78,1779031828218 |
| 58,2534578266532 | 80,3016421194227 |
| 53,9494482767622 | 82,0676597865827 |
| 49,7315457144966 | 84,0730730455222 |
| 42,6088408999317 | 84,1918726081281 |
| 59,9825558408614 | 85,7002070858551 |
| 56,9810533988051 | 87,2920544996764 |
| 53,0352352822315 | 90,5910444154961 |
| 47,6299567411805 | 93,3200004078775 |
| 68,350169487491 | 94,8349824377403 |
| 63,67413466217 | 97,1279910557192 |
| 57,8746208435369 | 102,003502552763 |
| 52,7447622106246 | 104,507854854094 |
| 71,3282305947596 | 106,221826405942 |
| 67,274094326561 | 105,707671261333 |
| 60,0636818820922 | 105,79930506829 |
| 53,1345066887794 | 107,733184029612 |
| 72,2390923307317 | 110,55066998749 |
| 69,1685093594435 | 112,2962613819 |
| 65,6374706822238 | 114,945962695954 |
| 58,1400830647319 | 116,602276795217 |
| 78,7915989931751 | 118,345653319227 |
| 72,8914941375442 | 120,268015941527 |
| 68,5054164049267 | 122,873146643073 |
| 61,518705014158 | 125,557766944926 |
| 78,1335731784645 | 127,189724815234 |
| 78,3712332002471 | 130,437555629647 |
| 74,0064716370768 | 132,01788788873 |
| 67,4050246926091 | 135,318921692506 |
| 85,8226347685586 | 137,102305690761 |
| 83,194883045778 | 137,248484168378 |
| 75,9200303847368 | 136,507419807885 |
| 68,1230183586928 | 137,053716236591 |
| 87,3372752177695 | 140,042390195142 |
| 84,8945443615665 | 142,874608602934 |
| 81,5863941417549 | 147,260748223411 |
| 75,4413753502906 | 149,884930670532 |
| 93,4285880304632 | 151,211266045902 |
| 89,5715078811253 | 152,972460754738 |
| 83,9502507313823 | 155,154623959009 |
| 78,5186832147435 | 159,721827677609 |
| 99,5712668155701 | 162,293164255201 |
| 96,5246178722633 | 164,233751056557 |
| 91,2884260850914 | 165,233709826198 |
| 85,0629128312343 | 165,894254490476 |
| 103,245514450378 | 168,818243314759 |
| 101,464306327094 | 170,302019861189 |
| 93,448754500595 | 170,518412604691 |
| 86,6978732780597 | 171,44559835787 |
| 106,096704118092 | 175,675134137059 |
| 104,169282387472 | 180,115427725381 |
| 98,4286143663242 | 182,973860207867 |
| 93,9338216380859 | 185,824959013781 |
| 112,356988777469 | 187,911635423744 |
| 107,346302585979 | 189,892834106359 |
| 103,195824208241 | 190,883162883682 |
| 96,8527952828484 | 192,307347799297 |
| 115,073115064688 | 195,729708746176 |
| 112,438837972484 | 198,815615253369 |
| 108,930227237007 | 202,418624128214 |
| 102,31749056783 | 204,468265962759 |
| 119,089070458272 | 204,889983330094 |
| 115,866482036584 | 206,530285279943 |
| 112,726044352273 | 209,086349307934 |
| 107,822665120148 | 212,44246054199 |
| 124,331462698487 | 217,012490547821 |
| 122,620589240846 | 220,498361057115 |
| 117,100246510859 | 222,853884309429 |
| 112,385301044006 | 224,746897731868 |
| 130,329423660117 | 227,790395142163 |
| 129,542132283685 | 231,579638478334 |
| 124,53648711341 | 233,973261182302 |
| 120,501665861038 | 238,221475199817 |
| 140,608330694059 | 240,896933126988 |
| 136,790970307066 | 243,586476483567 |
| 131,677048528135 | 245,967764990988 |
| 125,148978967354 | 249,668591902067 |
| 144,480036485479 | 253,684189954638 |
| 142,624849862326 | 258,814358216492 |
| 138,421236940235 | 260,441603126391 |
| 134,058046826819 | 263,442458276599 |
| 151,693002788131 | 268,162587887743 |
| 150,170209738746 | 274,084910633232 |
| 145,044687291824 | 277,417620161519 |
| 138,014911519266 | 279,713345827467 |
| 159,293081727329 | 283,689524849126 |
| 157,237621698171 | 287,740324093576 |
| 153,31320587926 | 290,992352107138 |
| 148,160638120915 | 295,504246416138 |
| 168,72344863903 | 300,745782365214 |
| 166,703175036287 | 304,214392616152 |
| 162,804331045101 | 308,33648336199 |
| 155,08848699932 | 312,074684634534 |
| Zadanie | ||||||||||||||||||
| Oblicz prognozę na okres 35, 36, 37 z najlepszego modelu średniej ruchomej (2, 5, 8 - wyrazowej). | ||||||||||||||||||
| Policz błedy ex post. | ||||||||||||||||||
| 1 | 261081,81 | |||||||||||||||||
| 2 | 253499,15 | dane kwartalne | ||||||||||||||||
| 3 | 337930,85 | Struktura | st. w. trendu | sezonow | rząd AR | |||||||||||||
| 4 | 336088,22 | Yt | 1 | 1 | ||||||||||||||
| 5 | 404564,99 | Xt | - | |||||||||||||||
| 6 | 458250,25 | |||||||||||||||||
| 7 | 642775,85 | |||||||||||||||||
| 8 | 633534,11 | |||||||||||||||||
| 9 | 657441,68 | |||||||||||||||||
| 10 | 837428,67 | |||||||||||||||||
| 11 | 767538,68 | |||||||||||||||||
| 12 | 1294972,53 | |||||||||||||||||
| 13 | 1028150,13 | |||||||||||||||||
| 14 | 1091291,53 | |||||||||||||||||
| 15 | 1462652,11 | |||||||||||||||||
| 16 | 1483307,18 | |||||||||||||||||
| 17 | 1666981,67 | |||||||||||||||||
| 18 | 1674585,3 | |||||||||||||||||
| 19 | 1915321,56 | |||||||||||||||||
| 20 | 2088865,45 | |||||||||||||||||
| 21 | 2177568 | |||||||||||||||||
| 22 | 2709432,58 | |||||||||||||||||
| 23 | 2583638,05 | |||||||||||||||||
| 24 | 3158578,86 | |||||||||||||||||
| 25 | 5001106,87 | |||||||||||||||||
| 26 | 5136984,68 | |||||||||||||||||
| 27 | 5157690,14 | |||||||||||||||||
| 28 | 5258448 | |||||||||||||||||
| 29 | 5631662,3 | |||||||||||||||||
| 30 | 5745434,49 | |||||||||||||||||
| 31 | 5795389,54 | |||||||||||||||||
| 32 | 6210795,52 | |||||||||||||||||
| 33 | 6589431,28 | |||||||||||||||||
| 34 | 6618815,45 | |||||||||||||||||
| 35 | 6677550,46 | |||||||||||||||||
| 36 | 6608391,84 | |||||||||||||||||
| 37 | 6831286,28 |
| Yt | Xt | |||||
| 24,4095 | 37,6239 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 24,1701 | 36,4510 | Yt | 0 | |||
| 26,1576 | 37,6512 | Xt | - | 3 | ||
| 24,4126288445955 | 37,3596285362865 | |||||
| 24,1706358303795 | 36,689723108206 | |||||
| 26,2830548131679 | 37,1377868716091 | |||||
| 25,833511395401 | 38,26166334817 | |||||
| 24,1476367882066 | 37,5004894487435 | |||||
| 26,8027208072648 | 39,3146352993753 | |||||
| 24,8949991789903 | 36,8289953446142 | |||||
| 26,0642564770508 | 36,0392899068324 | |||||
| 24,847808139859 | 37,5031454876087 | |||||
| 23,8113428963893 | 37,0415751956921 | |||||
| 24,3345437385441 | 37,6246307823314 | |||||
| 24,5699006396059 | 36,5924219305847 | |||||
| 25,7584694475673 | 38,4305273539118 | |||||
| 27,8235164268122 | 36,9624168350562 | |||||
| 26,2901868630302 | 37,7097239210903 | |||||
| 24,7862853124156 | 38,7167539323887 | |||||
| 23,2487571488515 | 39,2518861687491 | |||||
| 23,8529714575371 | 38,944113096748 | |||||
| 23,8450554738917 | 38,4774829221958 | |||||
| 24,4969718662921 | 38,385846448592 | |||||
| 26,3386500025094 | 38,5606301264644 | |||||
| 26,3575031603121 | 38,9032354260171 | |||||
| 24,923049510908 | 35,5701610038311 | |||||
| 25,7837663396406 | 35,7068412048109 | |||||
| 24,9357017715784 | 36,4787059388325 | |||||
| 25,9226582302985 | 38,7201437239766 | |||||
| 25,8268664615697 | 38,9023297750735 | |||||
| 26,113126971346 | 38,0475997944706 | |||||
| 26,6774551870804 | 39,2377300644091 | |||||
| 25,8207362733798 | 39,9024520219719 | |||||
| 28,1808168933452 | 40,1933702736118 | |||||
| 27,9954324557236 | 41,4428117578768 | |||||
| 24,5757963340824 | 41,2492077324152 | |||||
| 23,7678619396222 | 40,9254941120898 | |||||
| 24,5842567492195 | 38,6833964354031 | |||||
| 25,9136076184476 | 39,0916445483858 | |||||
| 25,3431881819229 | 38,3097068372344 | |||||
| 26,6296830556969 | 38,6245381797758 | |||||
| 25,540784677528 | 38,6936060493586 | |||||
| 25,8096642801967 | 38,983883716101 | |||||
| 26,087594482948 | 39,9151044085131 | |||||
| 24,9560857416711 | 39,3091065500664 | |||||
| 22,7507431487088 | 37,8437185093736 | |||||
| 23,8442918115629 | 37,8492421889415 | |||||
| 24,4091965669708 | 38,3939395561637 | |||||
| 22,9278289668591 | 37,0684926885059 | |||||
| 24,9532013392425 | 37,6434290421644 | |||||
| 25,1297522219984 | 37,9474173206177 | |||||
| 25,2184159570901 | 38,7966805673187 | |||||
| 24,5897953682134 | 39,4066477281437 | |||||
| 24,8461487566125 | 39,3600093429583 | |||||
| 23,8542371509295 | 41,2472638107543 | |||||
| 23,7730749249697 | 40,0401315437114 | |||||
| 24,6814341460988 | 40,8070562008614 | |||||
| 25,6132873092233 | 40,5402204214794 | |||||
| 26,889825192351 | 41,6240228044038 | |||||
| 25,9372757206708 | 40,9850685689138 | |||||
| 26,0772808847252 | 42,2043038983736 | |||||
| 27,0987245142833 | 41,2012983488175 | |||||
| 28,8286573757733 | 41,6390564650198 | |||||
| 27,3127008840488 | 41,3348626039824 | |||||
| 27,306137417151 | 42,5701748321319 | |||||
| 26,6297679444004 | 41,6071523874699 | |||||
| 25,8683617939467 | 43,368571361325 | |||||
| 27,0598159545285 | 43,0060535666096 | |||||
| 28,238206517465 | 43,1449730708693 | |||||
| 28,456984542289 | 42,4099856402395 | |||||
| 29,4308389931945 | 41,9497725920825 | |||||
| 28,3883937455817 | 42,0570646331475 | |||||
| 27,9438543310391 | 43,2213734294654 | |||||
| 27,3938976836124 | 43,726788929207 | |||||
| 28,4553285520827 | 42,1785724597343 | |||||
| 28,2345773379994 | 43,9517054687096 | |||||
| 27,324832598123 | 42,8681372333047 | |||||
| 28,4481321027054 | 42,5407794886488 | |||||
| 26,6326639499581 | 41,0660677694388 | |||||
| 25,1339111535563 | 41,061347061597 | |||||
| 25,945544179828 | 40,8450726700601 | |||||
| 27,6472995238777 | 42,6156341666274 | |||||
| 24,9330815505422 | 41,427532888675 | |||||
| 26,0783586200406 | 42,3305954491812 | |||||
| 28,4849558227767 | 43,0882903027858 | |||||
| 29,6946422141971 | 42,6301462386908 | |||||
| 28,1005222465473 | 42,509555744214 | |||||
| 27,416762561846 | 42,6892192575785 | |||||
| 26,357535056778 | 41,6042690300731 | |||||
| 27,5006176833199 | 41,8873160464746 | |||||
| 27,4761679930968 | 42,952926485391 | |||||
| 27,8234700797161 | 42,2806968991624 | |||||
| 27,4444695906714 | 41,9154328758198 | |||||
| 27,3447042234213 | 43,2872834981624 | |||||
| 25,7573307126995 | 42,2830605818109 | |||||
| 26,4409299220892 | 42,7905348233713 | |||||
| 25,1619589999512 | 42,6305823689336 | |||||
| 27,2323473291704 | 43,0269977520094 | |||||
| 27,7603628573546 | 42,9882663972114 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 59381,35 | |
| 55923,06 | |
| 57256,13 | |
| 57029,98 | |
| 57198,99 | |
| 57063,34 | |
| 58601,26 | |
| 57133,93 | |
| 57639,85 | |
| 59460,56 | |
| 59919,19 | |
| 57879,46 | |
| 57188,83 | |
| 48483,65 | |
| 54274,4 | |
| 58177,12 | |
| 51660,33 | |
| 57222,94 | |
| 59787,96 | |
| 62501,12 | |
| 66237,64 | |
| 53763,84 | |
| 55000,87 | |
| 59798,6 | |
| 53705,6 | |
| 55420,88 | |
| 55468,6 | |
| 50889,88 | |
| 51237,39 | |
| 51033,44 | |
| 51251,59 | |
| 50254,94 | |
| 52024,58 | |
| 57144,45 | |
| 57021,44 | |
| 57012,34 | |
| 58990,6 |
| Yt | Xt | dane miesięczne | ||||
| 28,6513 | 43,0021 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 28,2327 | 45,0807 | Yt | - | 2 | ||
| 28,1533 | 45,8185 | Xt | 1 | |||
| 28,9697098467971 | 46,1665068949498 | |||||
| 28,1644612009721 | 47,3699382916714 | |||||
| 29,2323929987249 | 48,5532054580456 | |||||
| 30,0570309957978 | 47,9738033833388 | |||||
| 28,9294639802122 | 47,7643560090827 | |||||
| 29,3585733070877 | 48,4839135288421 | |||||
| 29,0366451721466 | 46,4523942433623 | |||||
| 30,956537129877 | 48,0772394028535 | |||||
| 29,0390461255082 | 45,3520792089524 | |||||
| 27,138631009365 | 44,217540497555 | |||||
| 28,2579631448525 | 44,111300180648 | |||||
| 28,3254476595397 | 44,6195264158648 | |||||
| 28,6519647464998 | 44,6506978042023 | |||||
| 30,0303183129118 | 45,6459165711512 | |||||
| 27,9300117550914 | 46,8848540007785 | |||||
| 27,4447686964434 | 47,893547810972 | |||||
| 26,7787143686279 | 47,5044015725865 | |||||
| 28,1425857928554 | 46,6480344866878 | |||||
| 28,3380925178498 | 45,2042316015942 | |||||
| 29,2312559361302 | 44,4391689924456 | |||||
| 28,0015997978556 | 44,3950639786081 | |||||
| 26,8948077072924 | 45,7202427645797 | |||||
| 27,688155460343 | 47,2034310538411 | |||||
| 28,1371058053479 | 47,757818665957 | |||||
| 30,3071230429648 | 45,8621719628106 | |||||
| 28,1134186539128 | 45,7114625667052 | |||||
| 26,6852866945332 | 44,7943653956749 | |||||
| 27,4101496259041 | 45,8803236148544 | |||||
| 28,0637124388119 | 45,5634112742741 | |||||
| 28,8064762185167 | 46,3577707698858 | |||||
| 26,4311480250477 | 44,5469211212428 | |||||
| 26,4859800746492 | 46,0855016488566 | |||||
| 26,386405103272 | 45,1038231717097 | |||||
| 27,9331881621358 | 46,0454601734342 | |||||
| 28,7232483863255 | 45,8845227258021 | |||||
| 27,0705332414415 | 46,6367870531696 | |||||
| 26,0727522272677 | 46,6569370149555 | |||||
| 28,3204406964961 | 46,8959937797638 | |||||
| 28,6716563505941 | 46,950319961711 | |||||
| 26,9841723107635 | 46,2623027079646 | |||||
| 28,5694186469516 | 46,4518788573393 | |||||
| 28,324879837515 | 47,6855541344508 | |||||
| 29,3291831991743 | 47,0306355962793 | |||||
| 29,6216357558649 | 48,676671826635 | |||||
| 28,6804380035965 | 49,3745829479746 | |||||
| 27,1048619836478 | 48,9126241975194 | |||||
| 29,0827707200288 | 49,713115037577 | |||||
| 30,6569945379898 | 50,5289396922071 | |||||
| 30,9013213138915 | 51,6751734870935 | |||||
| 30,5769855581561 | 51,2159629924028 | |||||
| 30,8287013661326 | 51,8069419031283 | |||||
| 30,5363899309538 | 50,8075193421792 | |||||
| 28,9590143466829 | 50,6255015777654 | |||||
| 28,0828195470386 | 49,4055683686873 | |||||
| 30,7131270355513 | 51,1846876261062 | |||||
| 32,654621440972 | 50,3946827707168 | |||||
| 32,8245594814198 | 50,6229022765245 | |||||
| 30,3710582543628 | 50,1357086719085 | |||||
| 28,3931515543403 | 48,0174593319591 | |||||
| 29,4920345732758 | 46,2552077454431 | |||||
| 27,698273676071 | 46,9161207124719 | |||||
| 28,8990244069013 | 47,1877428847242 | |||||
| 29,9161721673761 | 49,0596403954875 | |||||
| 28,5394130127732 | 50,0345829602154 | |||||
| 30,8436924387215 | 52,3719933178306 | |||||
| 29,2268907270547 | 51,1455427996655 | |||||
| 28,3502511033596 | 51,5707070831054 | |||||
| 28,2861774233809 | 50,3324884261968 | |||||
| 28,7524991937025 | 50,6709966207166 | |||||
| 27,9505768903044 | 48,7297030836679 | |||||
| 30,3309269252644 | 49,9980231511764 | |||||
| 30,0020003320109 | 47,1246254916629 | |||||
| 29,6891564176815 | 49,614241623617 | |||||
| 28,2963760400872 | 49,6407279914338 | |||||
| 28,8434581647315 | 49,3868841836128 | |||||
| 28,5034470257389 | 47,5183005828744 | |||||
| 31,1543320515173 | 47,7872000065218 | |||||
| 29,2049013234987 | 47,5260333420528 | |||||
| 29,5238563349115 | 48,8526198906133 | |||||
| 29,9372345676016 | 49,6079419356795 | |||||
| 30,8166041671375 | 49,3325444601811 | |||||
| 28,9583899650095 | 48,9802852786899 | |||||
| 29,6062004591002 | 49,2873461181324 | |||||
| 31,3982819948436 | 49,8900843624501 | |||||
| 30,0372444802463 | 50,1144973971718 | |||||
| 30,0554300950944 | 49,8134545234117 | |||||
| 29,957672510735 | 50,7517050607085 | |||||
| 30,5223447231126 | 51,3376599140142 | |||||
| 31,6915098575935 | 52,5839165619388 | |||||
| 28,8270901488473 | 52,4895068992258 | |||||
| 28,8463995748588 | 52,1013471253143 | |||||
| 30,9546949586469 | 52,4238770325686 | |||||
| 30,3668454463059 | 52,1168289772903 | |||||
| 31,0365301124418 | 52,9257910710819 | |||||
| 30,1124118571166 | 52,1408479293225 | |||||
| 29,2806643508751 | 51,78548028346 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Wintersa |
| b) | policzyć prognozy oraz błędy prognoz |
| Yt | |
| 893,81 | |
| 900,53 | |
| 943,3 | |
| 986,98 | |
| 1025,2 | |
| 1054,01 | |
| 1091,46 | |
| 1090,32 | |
| 1185,13 | |
| 1199,28 | |
| 1260,66 | |
| 1199,28 | |
| 1183,57 | |
| 1172,7 | |
| 1235,36 | |
| 1224,79 | |
| 1263,23 | |
| 1315,93 | |
| 1321,33 | |
| 1336 | |
| 1368,27 | |
| 1377,34 | |
| 1426,64 | |
| 1494,62 | |
| 1118,66 | |
| 1533,98 | |
| 1605,39 | |
| 1693,08 | |
| 1684,07 | |
| 1701,06 | |
| 1771,26 | |
| 1794,83 | |
| 1828,18 | |
| 1908,62 | |
| 1861,25 | |
| 1925,81 | |
| 1838,99 | |
| 1785,39 | |
| 1865,38 | |
| 1888,33 | |
| 1892,83 | |
| 1957 | |
| 1968,13 | |
| 2000,76 | |
| 2029,93 | |
| 2039,84 | |
| 2078,94 | |
| 2128,7 | |
| 1931,24 | |
| 1952,38 | |
| 1967,7 | |
| 1963,64 | |
| 1991,77 | |
| 2024,15 | |
| 2065,78 | |
| 2098,56 | |
| 2081,35 | |
| 2098,78 | |
| 2147,78 |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | ||||
| 12,3805 | 25,9273 | Xt | 2 | + | 3 | |
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | |
| Oblicz prognozę na okres 35, 36, 37 z najlepszego modelu średniej ruchomej (2, 4,7 - wyrazowej). | |
| Policz błedy ex post. | |
| 1 | 59381,35 |
| 2 | 55923,06 |
| 3 | 57256,13 |
| 4 | 57029,98 |
| 5 | 57198,99 |
| 6 | 57063,34 |
| 7 | 58601,26 |
| 8 | 57133,93 |
| 9 | 57639,85 |
| 10 | 59460,56 |
| 11 | 59919,19 |
| 12 | 57879,46 |
| 13 | 57188,83 |
| 14 | 48483,65 |
| 15 | 54274,4 |
| 16 | 58177,12 |
| 17 | 51660,33 |
| 18 | 57222,94 |
| 19 | 59787,96 |
| 20 | 62501,12 |
| 21 | 66237,64 |
| 22 | 53763,84 |
| 23 | 55000,87 |
| 24 | 59798,6 |
| 25 | 53705,6 |
| 26 | 55420,88 |
| 27 | 55468,6 |
| 28 | 50889,88 |
| 29 | 51237,39 |
| 30 | 51033,44 |
| 31 | 51251,59 |
| 32 | 50254,94 |
| 33 | 52024,58 |
| 34 | 57144,45 |
| 35 | 57021,44 |
| 36 | 57012,34 |
| 37 | 56950,1 |
| Yt | Xt | dane kwartalne | ||||
| 89,5039 | 172,9332 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 88,5981 | 173,8236 | Yt | ||||
| 90,2334 | 175,2739 | Xt | 2 | - | 1 | |
| 91,2614896296605 | 179,672870311247 | |||||
| 91,4185575455556 | 182,429448124499 | |||||
| 91,5318006465489 | 181,3133792498 | |||||
| 93,7979788581459 | 185,12105169992 | |||||
| 93,8303256527339 | 187,766120679968 | |||||
| 95,6923597809714 | 187,925748271987 | |||||
| 93,6697251372527 | 189,469099308795 | |||||
| 93,8161518238878 | 192,589539723518 | |||||
| 95,7390602544308 | 194,119715889407 | |||||
| 95,8901711024209 | 196,161986355763 | |||||
| 97,0794991450229 | 198,182894542305 | |||||
| 96,6128092756613 | 200,067957816922 | |||||
| 99,2692922919425 | 202,795883126769 | |||||
| 98,5177228102685 | 205,184353250708 | |||||
| 99,7071363111752 | 206,658041300283 | |||||
| 101,329998888423 | 208,710816520113 | |||||
| 102,233774151163 | 209,939626608045 | |||||
| 101,981808289713 | 210,125650643218 | |||||
| 102,170890999382 | 212,311360257287 | |||||
| 103,452469679467 | 216,888744102915 | |||||
| 104,305899418814 | 219,150897641166 | |||||
| 105,345393142957 | 221,473859056466 | |||||
| 102,561764090607 | 223,305343622587 | |||||
| 103,367322439521 | 225,534937449035 | |||||
| 105,089418432717 | 228,702374979614 | |||||
| 107,80916872153 | 230,296749991846 | |||||
| 108,228789774095 | 231,088199996738 | |||||
| 108,102303794079 | 233,515679998695 | |||||
| 109,882621664252 | 235,482971999478 | |||||
| 111,310968661909 | 238,028388799791 | |||||
| 111,935836929587 | 239,141555519917 | |||||
| 114,372008420267 | 243,097322207967 | |||||
| 114,846266397371 | 245,323528883187 | |||||
| 115,344937578072 | 248,064811553275 | |||||
| 113,377133821796 | 248,97912462131 | |||||
| 114,567819502943 | 251,587249848524 | |||||
| 114,123156819057 | 252,71149993941 | |||||
| 114,440628172505 | 252,720299975764 | |||||
| 115,68342204645 | 256,632719990306 | |||||
| 116,944580114938 | 259,868987996122 | |||||
| 118,294302968048 | 261,263995198449 | |||||
| 118,30990597388 | 263,335998079379 | |||||
| 117,735578278899 | 266,306199231752 | |||||
| 118,499556096752 | 268,834379692701 | |||||
| 119,235075119288 | 269,47045187708 | |||||
| 119,020206913756 | 273,172380750832 | |||||
| 120,215024732264 | 275,238652300333 | |||||
| 121,043235596658 | 276,986060920133 | |||||
| 122,879937877735 | 280,277524368053 | |||||
| 124,50918065231 | 283,675109747221 | |||||
| 124,931242512625 | 285,237443898888 | |||||
| 127,444997078621 | 287,325777559555 | |||||
| 126,466084850858 | 288,086511023822 | |||||
| 127,63425752372 | 289,424004409529 | |||||
| 128,019560950623 | 291,597801763812 | |||||
| 130,142989016061 | 295,063220705525 | |||||
| 130,148845053577 | 297,21258828221 | |||||
| 132,647204492239 | 301,476335312884 | |||||
| 132,231958586364 | 303,435534125154 | |||||
| 133,038500560038 | 304,664813650061 | |||||
| 133,44576024199 | 307,036325460025 | |||||
| 136,389513887335 | 312,73113018401 | |||||
| 135,453408009551 | 312,820852073604 | |||||
| 137,576503610158 | 314,026440829442 | |||||
| 138,192266466143 | 317,287376331777 | |||||
| 139,068938230682 | 319,746550532711 | |||||
| 139,281431704165 | 322,904820213084 | |||||
| 139,257871017653 | 324,360328085234 | |||||
| 139,755014003376 | 325,659831234093 | |||||
| 141,993593177557 | 329,240732493637 | |||||
| 143,753236828443 | 333,421492997455 | |||||
| 142,938941619429 | 335,867897198982 | |||||
| 145,979293132587 | 340,091958879593 | |||||
| 145,036222298856 | 340,560283551837 | |||||
| 145,806273514869 | 344,218313420735 | |||||
| 144,897515379927 | 346,104825368294 | |||||
| 145,798826105792 | 349,124930147318 | |||||
| 146,048224287738 | 350,677172058927 | |||||
| 148,613094813699 | 353,324868823571 | |||||
| 148,580737147504 | 357,177347529428 | |||||
| 149,763397152713 | 358,109339011771 | |||||
| 151,207340984198 | 360,396835604709 | |||||
| 151,797306511256 | 363,890534241883 | |||||
| 153,09153985324 | 368,606613696753 | |||||
| 153,896112901189 | 370,689645478701 | |||||
| 153,315676487517 | 372,371358191481 | |||||
| 154,280529029452 | 374,644043276592 | |||||
| 156,136571678582 | 377,278817310637 | |||||
| 156,234984976439 | 379,847626924255 | |||||
| 156,93430810673 | 383,396250769702 | |||||
| 158,839213590527 | 385,173100307881 | |||||
| 159,055852618757 | 389,242640123152 | |||||
| 160,61990163815 | 392,764556049261 | |||||
| 160,752319094845 | 393,739122419704 | |||||
| 162,641302442374 | 398,714348967882 | |||||
| 163,409238273357 | 401,403239587153 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | wyrównać szereg czasowy za pomocą trendu pełzającego (k=6) |
| b) | wyznaczyć wartości prognoz za pomocą wag harmonicznych |
| c) | policzyć prognozy oraz błędy prognoz |
| yt | |
| 17,5 | |
| 19,1 | |
| 19 | |
| 18,7 | |
| 18,4 | |
| 18,3 | |
| 18,4 | |
| 18,2 | |
| 17,8 | |
| 17,7 | |
| 18 | |
| 18,5 | |
| 21,3 | |
| 21,3 | |
| 21,2 | |
| 20,7 | |
| 20,1 | |
| 19,8 | |
| 19,8 | |
| 19,6 | |
| 19,2 | |
| 19 | |
| 19,1 | |
| 19,6 | |
| 19,9 | |
| 19,9 | |
| 19,7 | |
| 19,2 | |
| 18,7 | |
| 18,3 | |
| 18,2 | |
| 18 | |
| 17,7 | |
| 17,4 | |
| 17,5 | |
| 17,9 |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | 1 | |||
| 12,3805 | 25,9273 | Xt | + | 3 | ||
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | -0,276 | y2t + | 0,363 | y1t-1 + | -0,465 | y2t-1 + | 0,281 | x1t + | -0,468 | x2t + | 0,097 | x3t |
| y2t | = | -0,423 | y1t + | -0,159 | y1t-1 + | 0,118 | y2t-1 + | -0,182 | x1t + | -0,374 | x2t + | -0,102 | x3t |
| Yt | Xt | dane kwartalne | ||||
| 46,2189 | 30,8388 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 43,3975 | 28,2399 | Yt | ||||
| 43,2245 | 27,9390 | Xt | 2 | - | 2 | |
| 46,8988617623156 | 29,0100858108434 | |||||
| 48,5993962034164 | 30,3426698712444 | |||||
| 45,5933565328561 | 31,7097545855337 | |||||
| 47,1436354404008 | 30,9708502613758 | |||||
| 50,1823058443531 | 32,4094133487496 | |||||
| 47,3541218490205 | 31,8116592395744 | |||||
| 45,4704719052158 | 30,0826561282022 | |||||
| 47,9460443231027 | 30,4576655939118 | |||||
| 49,0320658579435 | 32,5240434644574 | |||||
| 49,5019185798731 | 34,2700341875554 | |||||
| 50,7806762138098 | 35,7993665455059 | |||||
| 49,8975927943536 | 33,9113529068319 | |||||
| 49,2608473975658 | 31,63362041658 | |||||
| 50,058416878596 | 32,1952831288732 | |||||
| 50,4154144804219 | 33,7877700235793 | |||||
| 51,3207233746254 | 35,1404357649562 | |||||
| 51,7539226422554 | 36,5743570260376 | |||||
| 49,7524026565588 | 36,1954456122439 | |||||
| 50,2468394417189 | 36,3653091181556 | |||||
| 52,5532075695799 | 34,9677081378114 | |||||
| 53,2142831708755 | 35,9885320492057 | |||||
| 51,9054210722297 | 34,8094991793194 | |||||
| 52,963089944333 | 36,4120566058413 | |||||
| 53,166856682627 | 35,8523299523611 | |||||
| 54,719107997753 | 36,5222283243163 | |||||
| 55,445724691714 | 38,6551378460769 | |||||
| 55,1037763324366 | 40,5997651625273 | |||||
| 55,2676187845834 | 39,7171504753384 | |||||
| 54,6501481867252 | 38,0219392677259 | |||||
| 54,2172591259695 | 36,9894672972728 | |||||
| 54,0443486516918 | 38,4339114010006 | |||||
| 57,7942206624476 | 41,5426610617913 | |||||
| 59,423195726055 | 43,4127181828537 | |||||
| 59,4715160631122 | 43,4361283032811 | |||||
| 57,9431645161223 | 42,8816225391553 | |||||
| 57,7714343096349 | 41,5999944560963 | |||||
| 57,432589834994 | 41,9995071036053 | |||||
| 56,5290774509161 | 44,4280271900852 | |||||
| 57,2811200250627 | 42,3786561916175 | |||||
| 59,8494603724024 | 43,7018184580982 | |||||
| 58,3694643197758 | 43,8090704440217 | |||||
| 57,605002450646 | 43,4245319275759 | |||||
| 59,3284990641567 | 43,8868641716945 | |||||
| 60,4878809363919 | 45,0461821491558 | |||||
| 59,2157922506762 | 46,3298018357312 | |||||
| 60,8038681330632 | 46,5387984253496 | |||||
| 60,2810355138212 | 44,7473981634522 | |||||
| 58,9000217593574 | 44,1716293442767 | |||||
| 60,54560925733 | 45,2989212756128 | |||||
| 63,7534065672284 | 48,0656631552183 | |||||
| 63,1516087716532 | 48,7684556984077 | |||||
| 62,5296610732855 | 48,6826637267981 | |||||
| 61,9027076615569 | 49,3814023293956 | |||||
| 61,6662184088422 | 50,2953061398577 | |||||
| 61,0409905979218 | 48,9988733661421 | |||||
| 62,7743888068141 | 49,7125989003564 | |||||
| 63,2403166884302 | 50,9916298837926 | |||||
| 64,9361027940364 | 51,2639713585123 | |||||
| 65,0461730559102 | 51,7438679974415 | |||||
| 63,2560460938128 | 51,3395890548042 | |||||
| 63,2459604665561 | 50,9684251393863 | |||||
| 67,424567991769 | 51,5228719756487 | |||||
| 66,1641610361804 | 53,4940603271996 | |||||
| 64,9999876338834 | 55,4617834387802 | |||||
| 66,2475051033236 | 54,3561442762663 | |||||
| 66,9210756825377 | 54,3187976178743 | |||||
| 66,4506531707824 | 53,5901606220055 | |||||
| 65,496345325953 | 53,8291633882541 | |||||
| 65,1131653740745 | 54,9048901229757 | |||||
| 66,7684663302001 | 55,1465277307813 | |||||
| 69,7360839626199 | 56,8032733623567 | |||||
| 68,1792634874231 | 55,1573902613371 | |||||
| 69,5092359898288 | 55,2943838379933 | |||||
| 68,2421590139043 | 55,9204025820605 | |||||
| 69,4491201092285 | 56,542948272245 | |||||
| 69,7284740110071 | 57,0068127577473 | |||||
| 70,4136824646277 | 57,8432496215251 | |||||
| 71,2561991781349 | 60,7909196319687 | |||||
| 71,4000667596003 | 60,888083893768 | |||||
| 72,3748754117023 | 59,8125608728502 | |||||
| 69,8228915400785 | 58,3923190534879 | |||||
| 69,2724670544454 | 58,7552089883015 | |||||
| 72,215977612038 | 61,0520386704159 | |||||
| 75,5027793714555 | 62,7146334739705 | |||||
| 73,8181105023535 | 61,678447963613 | |||||
| 72,5470498964745 | 62,0739701849409 | |||||
| 74,675170420771 | 65,2718599440134 | |||||
| 75,7053001230291 | 66,189783886833 | |||||
| 75,6118959830715 | 66,4238447431778 | |||||
| 75,4956062677545 | 64,9906477654912 | |||||
| 74,8357815835639 | 65,1694755385727 | |||||
| 76,3023413115458 | 65,6335837708044 | |||||
| 77,9787541176715 | 66,513938424134 | |||||
| 77,2037063957848 | 68,706813388572 | |||||
| 78,52703663732 | 67,5286140023468 | |||||
| 78,8070086659389 | 66,745614446214 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | -0,233 | y2t + | 0,137 | y1t-1 + | -0,082 | y2t-1 + | 0,099 | y3t-1 + | 0,192 | x1t + | 0,418 | x2t |
| y2t | = | -0,472 | y3t + | -0,429 | y1t-1 + | -0,154 | y2t-1 + | -0,089 | y3t-1 + | -0,318 | x1t + | -0,376 | x2t |
| y3t | = | 0,272 | y1t + | 0,253 | y1t-1 + | 0,366 | y2t-1 + | 0,139 | y3t-1 + | -0,036 | x1t + | -0,324 | x2t |
| Yt | Xt | dane kwartalne | ||||
| 48,1183107138122 | 64,1442 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 44,6353997167258 | 65,9714 | Yt | 1 | + | 1 | |
| 39,0506105076807 | 67,1621 | Xt | ||||
| 33,4033278345713 | 68,190702584866 | |||||
| 51,9950409479241 | 69,6209053537098 | |||||
| 48,9929799569888 | 72,7457716429085 | |||||
| 43,4407589077525 | 76,0440236799703 | |||||
| 37,2680251252945 | 78,1779031828218 | |||||
| 58,2534578266532 | 80,3016421194227 | |||||
| 53,9494482767622 | 82,0676597865827 | |||||
| 49,7315457144966 | 84,0730730455222 | |||||
| 42,6088408999317 | 84,1918726081281 | |||||
| 59,9825558408614 | 85,7002070858551 | |||||
| 56,9810533988051 | 87,2920544996764 | |||||
| 53,0352352822315 | 90,5910444154961 | |||||
| 47,6299567411805 | 93,3200004078775 | |||||
| 68,350169487491 | 94,8349824377403 | |||||
| 63,67413466217 | 97,1279910557192 | |||||
| 57,8746208435369 | 102,003502552763 | |||||
| 52,7447622106246 | 104,507854854094 | |||||
| 71,3282305947596 | 106,221826405942 | |||||
| 67,274094326561 | 105,707671261333 | |||||
| 60,0636818820922 | 105,79930506829 | |||||
| 53,1345066887794 | 107,733184029612 | |||||
| 72,2390923307317 | 110,55066998749 | |||||
| 69,1685093594435 | 112,2962613819 | |||||
| 65,6374706822238 | 114,945962695954 | |||||
| 58,1400830647319 | 116,602276795217 | |||||
| 78,7915989931751 | 118,345653319227 | |||||
| 72,8914941375442 | 120,268015941527 | |||||
| 68,5054164049267 | 122,873146643073 | |||||
| 61,518705014158 | 125,557766944926 | |||||
| 78,1335731784645 | 127,189724815234 | |||||
| 78,3712332002471 | 130,437555629647 | |||||
| 74,0064716370768 | 132,01788788873 | |||||
| 67,4050246926091 | 135,318921692506 | |||||
| 85,8226347685586 | 137,102305690761 | |||||
| 83,194883045778 | 137,248484168378 | |||||
| 75,9200303847368 | 136,507419807885 | |||||
| 68,1230183586928 | 137,053716236591 | |||||
| 87,3372752177695 | 140,042390195142 | |||||
| 84,8945443615665 | 142,874608602934 | |||||
| 81,5863941417549 | 147,260748223411 | |||||
| 75,4413753502906 | 149,884930670532 | |||||
| 93,4285880304632 | 151,211266045902 | |||||
| 89,5715078811253 | 152,972460754738 | |||||
| 83,9502507313823 | 155,154623959009 | |||||
| 78,5186832147435 | 159,721827677609 | |||||
| 99,5712668155701 | 162,293164255201 | |||||
| 96,5246178722633 | 164,233751056557 | |||||
| 91,2884260850914 | 165,233709826198 | |||||
| 85,0629128312343 | 165,894254490476 | |||||
| 103,245514450378 | 168,818243314759 | |||||
| 101,464306327094 | 170,302019861189 | |||||
| 93,448754500595 | 170,518412604691 | |||||
| 86,6978732780597 | 171,44559835787 | |||||
| 106,096704118092 | 175,675134137059 | |||||
| 104,169282387472 | 180,115427725381 | |||||
| 98,4286143663242 | 182,973860207867 | |||||
| 93,9338216380859 | 185,824959013781 | |||||
| 112,356988777469 | 187,911635423744 | |||||
| 107,346302585979 | 189,892834106359 | |||||
| 103,195824208241 | 190,883162883682 | |||||
| 96,8527952828484 | 192,307347799297 | |||||
| 115,073115064688 | 195,729708746176 | |||||
| 112,438837972484 | 198,815615253369 | |||||
| 108,930227237007 | 202,418624128214 | |||||
| 102,31749056783 | 204,468265962759 | |||||
| 119,089070458272 | 204,889983330094 | |||||
| 115,866482036584 | 206,530285279943 | |||||
| 112,726044352273 | 209,086349307934 | |||||
| 107,822665120148 | 212,44246054199 | |||||
| 124,331462698487 | 217,012490547821 | |||||
| 122,620589240846 | 220,498361057115 | |||||
| 117,100246510859 | 222,853884309429 | |||||
| 112,385301044006 | 224,746897731868 | |||||
| 130,329423660117 | 227,790395142163 | |||||
| 129,542132283685 | 231,579638478334 | |||||
| 124,53648711341 | 233,973261182302 | |||||
| 120,501665861038 | 238,221475199817 | |||||
| 140,608330694059 | 240,896933126988 | |||||
| 136,790970307066 | 243,586476483567 | |||||
| 131,677048528135 | 245,967764990988 | |||||
| 125,148978967354 | 249,668591902067 | |||||
| 144,480036485479 | 253,684189954638 | |||||
| 142,624849862326 | 258,814358216492 | |||||
| 138,421236940235 | 260,441603126391 | |||||
| 134,058046826819 | 263,442458276599 | |||||
| 151,693002788131 | 268,162587887743 | |||||
| 150,170209738746 | 274,084910633232 | |||||
| 145,044687291824 | 277,417620161519 | |||||
| 138,014911519266 | 279,713345827467 | |||||
| 159,293081727329 | 283,689524849126 | |||||
| 157,237621698171 | 287,740324093576 | |||||
| 153,31320587926 | 290,992352107138 | |||||
| 148,160638120915 | 295,504246416138 | |||||
| 168,72344863903 | 300,745782365214 | |||||
| 166,703175036287 | 304,214392616152 | |||||
| 162,804331045101 | 308,33648336199 | |||||
| 155,08848699932 | 312,074684634534 |
| Zadanie | ||||
| Wiedząc, że dla poniższych danych (z pominięciem ostatnich dwóch obserwacji) pominięciemzachodzi zależność | ||||
| Y1t=f1(stała, Y2t, Y1,t-1, X1,t-1) | ||||
| Y2t=f2(stała, Y1t, X2t) | ||||
| Wyznaczyć prognozę na dwa okresy w przód oraz błędy prognoz | ||||
| t | Y1t | Y2t | X1t | X2t |
| 1945 | 6509198,48 | 6474855,36 | 0,742 | 3682771 |
| 1946 | 6339875,00496 | 6341607,889 | 0,807730426165 | 3372076 |
| 1947 | 6953428,1457 | 6926832,09882 | 0,644349516394 | 3873411 |
| 1948 | 6600331,46847 | 6414101,86325 | 0,82472950017 | 3946958 |
| 1949 | 7634026,84837 | 7271796,75194 | 0,76847716593 | 4697254 |
| 1950 | 7306971,87537 | 7159651,92818 | 0,749848537983 | 4610003 |
| 1951 | 6935406,25422 | 7068456,90156 | 0,810677074964 | 4760705 |
| 1952 | 7061308,69756 | 7241027,30883 | 0,815996411571 | 4679684 |
| 1953 | 7034487,62036 | 7050294,56867 | 0,783204476569 | 4374679 |
| 1954 | 7073328,74343 | 6990649,88967 | 0,783589199064 | 4284740 |
| 1955 | 6286323,74365 | 6731237,79492 | 0,794555187683 | 3656541 |
| 1956 | 6063944,42719 | 6393813,83286 | 0,807966303542 | 3800250 |
| 1957 | 6519698,0999 | 6470789,21674 | 0,80062399568 | 3816152 |
| 1958 | 5890150,08824 | 6384963,24416 | 0,80446891118 | 3375579 |
| 1959 | 6721662,92166 | 6896814,7976 | 0,768115157688 | 4039112 |
| 1960 | 6493092,57772 | 6609261,94415 | 0,712501525132 | 4220708 |
| 1961 | 6982293,79833 | 6744356,17306 | 0,682980965396 | 5091885 |
| 1962 | 6842215,82456 | 6639142,07121 | 0,673677497317 | 5170697 |
| 1963 | 6988981,66464 | 6805758,69507 | 0,665687426888 | 5213613 |
| 1964 | 6868563,89728 | 6766117,49528 | 0,670430678267 | 4830838 |
| 1965 | 6276943,81109 | 6254636,54304 | 0,685727966964 | 4477061 |
| 1966 | 6621595,13466 | 6586143,2531 | 0,707485878838 | 4307498 |
| 1967 | 6222740,97818 | 6158964,08652 | 0,719464878452 | 4029253 |
| 1968 | 6068632,80452 | 5800068,02347 | 0,746967010062 | 4078010 |
| 1969 | 6461289,78391 | 6443744,38285 | 0,732964428904 | 4183083 |
| 1970 | 6088310,79024 | 6485737,1911 | 0,725062236396 | 3865410 |
| 1971 | 8367297,55522 | 8175238,8266 | 0,723615006384 | 4405464 |
| 1972 | 6981261,03108 | 7227665,89382 | 0,692424742747 | 4571120 |
| 1973 | 7661561,7858 | 7770823,10773 | 0,662599728842 | 5625186 |
| 1974 | 7398131,0931 | 7303556,04591 | 0,638399637127 | 5469644 |
| 1975 | 7615026,69248 | 7675950,76977 | 0,632608970379 | 5560707 |
| 1976 | 7337132,27949 | 7341841,57474 | 0,636053053104 | 5143591 |
| 1977 | 6850299,37186 | 6856237,55269 | 0,662975628632 | 4866015 |
| 1978 | 6666779,6971 | 6693060,87266 | 0,634948103302 | 4641908 |
| 1979 | 6077734,90826 | 6167936,84623 | 0,671543160086 | 4034080 |
| 1980 | 6151785,63012 | 5325238,98163 | 0,581961502669 | 4192383 |
| 1981 | 6413475,62371 | 6702529,84052 | 0,744232898991 | 4366639 |
| 1982 | 5900684,53105 | 5988147,64222 | 0,663957489566 | 4073096 |
| 1983 | 6750391,63685 | 6658125,18344 | 0,636134191705 | 4737737 |
| 1984 | 6523781,29053 | 6439498,49835 | 0,611746149009 | 4396623 |
| 1985 | 6814154,31811 | 6743335,02724 | 0,609078651266 | 5010867 |
| 1986 | 6383933,74491 | 6395161,37375 | 0,615028675427 | 4686087 |
| 1987 | 7274048,81343 | 6499463,82555 | 0,609455995678 | 4690306 |
| 1988 | 5898660,47846 | 5851134,8492 | 0,614595268227 | 4459734 |
| 1989 | 5626432,81348 | 5639227,10813 | 0,632070958935 | 4081197 |
| 1990 | 6008598,32091 | 5666399,65378 | 0,645162341131 | 3870941 |
| 1991 | 5337588,71212 | 5393175,8508 | 0,689241030335 | 3597116 |
| 1992 | 5854002,80708 | 6009275,91272 | 0,704642502168 | 3853923 |
| 1993 | 5983520,66474 | 6060862,38064 | 0,709750595675 | 4043266 |
| 1994 | 5648007,76522 | 5860964,99577 | 0,711677396329 | 3835997 |
| 1995 | 6248845,75048 | 6455894,14309 | 0,721812555636 | 4262760 |
| 1996 | 6115163,66588 | 6572079,62051 | 0,728250358326 | 4280504 |
| 1997 | 6586995,54621 | 6488150,37236 | 0,701250079203 | 4820718 |
| 1998 | 6602481,23896 | 6449379,69735 | 0,708639199131 | 4707966 |
| 1999 | 6748075,63643 | 6647158,72696 | 0,728981539973 | 4770630 |
| 2000 | 7288913,81447 | 6250152,61535 | 0,708769191001 | 4485846 |
| 2001 | 6112494,63519 | 5924173,81666 | 0,723738705019 | 4122820 |
| 2002 | 6078912,19481 | 6165449,36443 | 0,762740390135 | 3983241 |
| 2003 | 5460132,61068 | 5658751,04867 | 0,786710938937 | 3589462 |
| 2004 | 5885756,22934 | 6433215,97706 | 0,840068394861 | 3850665 |
| Yt | Xt | dane kwartalne | ||||
| 79,0589 | 69,2947 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 80,1352 | 70,0700 | Yt | 1 | - | 3 | |
| 80,1362 | 70,5329 | Xt | ||||
| 78,8911120985945 | 71,2182710202372 | |||||
| 78,4386455751666 | 69,761155825782 | |||||
| 81,188972193915 | 69,9517206699525 | |||||
| 80,193799473351 | 68,947132138654 | |||||
| 83,1800710918659 | 71,7619242290768 | |||||
| 83,5322609860443 | 72,9046041048921 | |||||
| 82,1737763900257 | 74,8314131817938 | |||||
| 84,1020356975103 | 75,3327175852988 | |||||
| 83,9473094410644 | 75,7488770369916 | |||||
| 84,5995755749031 | 75,0621968917746 | |||||
| 83,8431972452081 | 75,9453470094456 | |||||
| 83,5112195175799 | 77,1751741499021 | |||||
| 83,7109826478529 | 77,2423031011532 | |||||
| 84,0807831209888 | 75,9016325108464 | |||||
| 84,6181291254505 | 74,9959415171312 | |||||
| 84,8796143937486 | 77,8575160576533 | |||||
| 85,3513201421102 | 78,2526446335048 | |||||
| 87,5233636523255 | 80,6593148203921 | |||||
| 86,6199523597888 | 80,6604025208725 | |||||
| 85,8528140851528 | 80,0105258364539 | |||||
| 87,7764813774519 | 79,9175670771688 | |||||
| 87,0050270185911 | 81,6325966194366 | |||||
| 87,6211714777254 | 81,8586108027381 | |||||
| 89,6721568590696 | 82,378178914142 | |||||
| 89,8741726660773 | 81,5978009188042 | |||||
| 88,3447424384628 | 82,2656990775061 | |||||
| 90,8159688565017 | 83,4467289867326 | |||||
| 93,5693145069823 | 85,6074006597104 | |||||
| 92,9764721237782 | 85,8407288671042 | |||||
| 92,3077499468051 | 85,6575199430888 | |||||
| 91,8698590215495 | 87,4648324133205 | |||||
| 90,8946702230938 | 88,6575847120888 | |||||
| 91,4193252823398 | 88,374196333134 | |||||
| 92,406095217958 | 87,5726935483582 | |||||
| 92,9193494403658 | 86,5756269505972 | |||||
| 94,1591899454568 | 88,6744714460747 | |||||
| 93,9960302071192 | 90,6145392320135 | |||||
| 92,5579805282101 | 90,1268588839795 | |||||
| 96,4299508099062 | 91,1168255259803 | |||||
| 96,9929465607193 | 92,1660043145944 | |||||
| 95,8899936659485 | 91,492732809824 | |||||
| 97,6070222439199 | 93,630021241039 | |||||
| 99,7598714469735 | 94,5288417447977 | |||||
| 99,5629369412255 | 95,4575707249428 | |||||
| 98,8087394680593 | 95,3670828095409 | |||||
| 96,9176746470958 | 93,5556396767015 | |||||
| 99,1320330929063 | 95,4424746498747 | |||||
| 100,834757855876 | 96,0300463842317 | |||||
| 99,6642952528627 | 96,9756826090123 | |||||
| 99,6980224915469 | 98,2521292726159 | |||||
| 99,9318447383575 | 99,2927774472262 | |||||
| 99,9339264695137 | 98,429002504012 | |||||
| 99,6482119557823 | 98,6185107739179 | |||||
| 102,124088284528 | 99,7054465401377 | |||||
| 102,131898451287 | 100,290828268529 | |||||
| 101,88326228937 | 100,105211171915 | |||||
| 102,759463767284 | 100,966276512929 | |||||
| 106,067746220149 | 103,115379090284 | |||||
| 105,632542120594 | 103,644194758027 | |||||
| 103,788686865126 | 104,334154694505 | |||||
| 104,801968022597 | 104,167490382943 | |||||
| 106,699671189916 | 105,861891390258 | |||||
| 105,216659906142 | 104,727247820003 | |||||
| 106,448842488233 | 103,410306917899 | |||||
| 105,379038670625 | 104,279435714528 | |||||
| 107,713870978149 | 108,48959223301 | |||||
| 108,784284916641 | 109,101200277296 | |||||
| 107,717350637526 | 108,289473300903 | |||||
| 108,696855085211 | 108,551391199714 | |||||
| 108,561993810774 | 107,595954519438 | |||||
| 105,295838671659 | 107,105571683721 | |||||
| 108,031953030412 | 109,90862837083 | |||||
| 113,446624636215 | 113,056131186092 | |||||
| 111,735402988895 | 111,740430481933 | |||||
| 111,421630621858 | 113,640168862916 | |||||
| 113,032351103396 | 114,158156011268 | |||||
| 112,256634145001 | 113,218301662721 | |||||
| 110,593561126417 | 114,048218759398 | |||||
| 113,885950983322 | 115,87417246649 | |||||
| 114,725082603282 | 116,061603222784 | |||||
| 114,706867952584 | 114,786713269353 | |||||
| 113,751570095851 | 115,775467999433 | |||||
| 112,107445230224 | 116,629262291862 | |||||
| 116,050088194098 | 117,91108640453 | |||||
| 116,435071383114 | 117,531175566426 | |||||
| 115,713192083722 | 118,864498334686 | |||||
| 116,228957855089 | 118,69963860771 | |||||
| 117,755705774877 | 120,067017691522 | |||||
| 118,990162438018 | 121,636196940982 | |||||
| 119,032084568722 | 120,864700782078 | |||||
| 119,049574452391 | 121,622171771062 | |||||
| 120,318108136892 | 124,230149926912 | |||||
| 119,216732419515 | 125,751256240414 | |||||
| 121,406305932349 | 126,454109397525 | |||||
| 125,590362600364 | 128,477194082102 | |||||
| 123,801763366421 | 128,021502098461 | |||||
| 56,4788214503041 | 68,5715103364051 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 59381,35 | |
| 55923,06 | |
| 57256,13 | |
| 57029,98 | |
| 57198,99 | |
| 57063,34 | |
| 58601,26 | |
| 57133,93 | |
| 57639,85 | |
| 59460,56 | |
| 59919,19 | |
| 57879,46 | |
| 57188,83 | |
| 48483,65 | |
| 54274,4 | |
| 58177,12 | |
| 51660,33 | |
| 57222,94 | |
| 59787,96 | |
| 62501,12 | |
| 66237,64 | |
| 53763,84 | |
| 55000,87 | |
| 59798,6 | |
| 53705,6 | |
| 55420,88 | |
| 55468,6 | |
| 50889,88 | |
| 51237,39 | |
| 51033,44 | |
| 51251,59 | |
| 50254,94 | |
| 52024,58 | |
| 57144,45 | |
| 57021,44 | |
| 57012,34 | |
| 58990,6 |
| Yt | Xt | dane kwartalne | ||||
| 20,1127432256159 | 25,4327 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 20,684535774468 | 24,1043 | Yt | 1 | + | 3 | |
| 26,8776559015158 | 15,6247 | Xt | ||||
| 20,9937015411991 | 25,7428290413533 | |||||
| 21,9107551616107 | 25,4134602107025 | |||||
| 24,0340909764375 | 22,1911901999061 | |||||
| 29,833763790308 | 13,1606901302175 | |||||
| 22,3175596971194 | 24,0207330284325 | |||||
| 23,5741947621081 | 25,7876517282962 | |||||
| 25,0091875525615 | 23,0042830396848 | |||||
| 33,0139235606183 | 13,716866308029 | |||||
| 27,6501690333759 | 22,1946313571301 | |||||
| 27,1686563424295 | 22,1683304941821 | |||||
| 30,4406889833579 | 18,1123605692742 | |||||
| 37,0689633410425 | 10,2096794660749 | |||||
| 29,1358234337453 | 22,807562633373 | |||||
| 30,1417400082239 | 25,4524886939294 | |||||
| 29,9050445876062 | 24,4852755402514 | |||||
| 32,5440754981415 | 18,6072010398657 | |||||
| 25,570279783942 | 29,7035736775589 | |||||
| 25,8670810870127 | 29,7982369482151 | |||||
| 31,6951989003955 | 22,1635628073411 | |||||
| 41,3546739390274 | 7,60858723835225 | |||||
| 35,7570263657822 | 14,8219330547566 | |||||
| 35,5797705917128 | 15,2895643730935 | |||||
| 36,8605516836467 | 13,7509632476687 | |||||
| 41,9319748875703 | 9,00383326048572 | |||||
| 30,9202843132245 | 23,9009662938754 | |||||
| 30,0716352082217 | 28,5761961357634 | |||||
| 28,7521098453657 | 27,3692441527337 | |||||
| 35,8871466410647 | 18,2005141221868 | |||||
| 28,5487025679899 | 27,4085028580385 | |||||
| 28,3259688940063 | 25,1958418628936 | |||||
| 33,9601646527457 | 20,524394408395 | |||||
| 44,0694871532561 | 8,48697337682783 | |||||
| 35,8741162571666 | 19,614202435369 | |||||
| 35,2816270731357 | 20,8284478574454 | |||||
| 39,1839343352869 | 17,5486343800805 | |||||
| 46,7164965254407 | 6,87441193642793 | |||||
| 39,2790977073096 | 16,8055881562123 | |||||
| 37,7904573766526 | 19,3680703071545 | |||||
| 38,6783764085632 | 18,6492831508561 | |||||
| 43,0195493944622 | 14,1440897649308 | |||||
| 33,5609564092565 | 27,9631887881187 | |||||
| 32,2595471018711 | 29,9551212725523 | |||||
| 34,5372755061167 | 26,0660241267768 | |||||
| 42,7647540561202 | 14,0771294575458 | |||||
| 35,6265114808997 | 23,7255854179742 | |||||
| 38,6913107815599 | 22,5551201569675 | |||||
| 42,2299506615262 | 18,3019653749712 | |||||
| 50,968512975726 | 7,46873645868318 | |||||
| 45,6308333002696 | 16,824009496419 | |||||
| 43,6889712964152 | 19,2212523814556 | |||||
| 47,1278168899176 | 16,9113952635518 | |||||
| 52,4382118072217 | 7,75820527837286 | |||||
| 44,7789079557179 | 18,9423727082 | |||||
| 41,7427600882115 | 23,1369115825844 | |||||
| 41,4431925708859 | 23,608323094755 | |||||
| 45,7899755469526 | 16,5631965272821 | |||||
| 38,6278126203748 | 28,7166236583718 | |||||
| 38,7892597416758 | 28,7312209788411 | |||||
| 41,0694755072774 | 23,072292273611 | |||||
| 52,5162779393891 | 9,10296875682071 | |||||
| 48,4139183731503 | 15,7141869646632 | |||||
| 47,5983953902644 | 15,8714272623225 | |||||
| 48,8777353856598 | 13,9929153515191 | |||||
| 53,845677273768 | 8,6723800263403 | |||||
| 43,8743613465002 | 22,8856842257773 | |||||
| 41,3733012969048 | 25,3930527375374 | |||||
| 43,0889587454245 | 23,0060685768603 | |||||
| 52,2681511430237 | 12,9275622591928 | |||||
| 46,5889247802472 | 22,7618378955342 | |||||
| 42,7113736952779 | 24,3695345995812 | |||||
| 44,9765026631449 | 21,7019012533492 | |||||
| 51,4068408723277 | 12,2260608657356 | |||||
| 46,1191480548259 | 22,1165862571627 | |||||
| 44,7739326417791 | 23,0212832322982 | |||||
| 48,0130037549099 | 20,5348255402308 | |||||
| 55,5216909744394 | 10,7759659553009 | |||||
| 48,3087952206135 | 23,2323025422737 | |||||
| 49,2080046046366 | 24,5091147078671 | |||||
| 50,6569415589217 | 21,865611244541 | |||||
| 58,1291762731406 | 11,8844747541853 | |||||
| 49,7233393801225 | 22,7551094866095 | |||||
| 48,4975476846585 | 24,2848478998085 | |||||
| 48,8054581789456 | 23,415858101745 | |||||
| 57,5297042980419 | 13,0564098529644 | |||||
| 51,7636354053612 | 23,8162834731725 | |||||
| 48,8416044030217 | 25,6088846894081 | |||||
| 49,1023643158868 | 24,6671603771976 | |||||
| 55,2603213378133 | 15,386060383049 | |||||
| 47,528507932783 | 25,1045522734005 | |||||
| 48,6658256620266 | 25,7922292926967 | |||||
| 51,654341441262 | 21,9474698222543 | |||||
| 60,2570674752622 | 11,3550453521798 | |||||
| 52,7169346488304 | 22,5385497234589 | |||||
| 51,4747665002755 | 25,3675387405723 | |||||
| 53,6892534694114 | 23,1769672338028 | |||||
| 60,0874574778528 | 15,2997627075693 | |||||
| 50,540239086024 | 26,2299498216884 |
| Zadanie |
| Dokaonaj identyfikacji modelu ARMA (do p=3 i q=3) dla poniższego szeregu |
| Yt |
| 0 |
| 2,5294047 |
| 0,86550182 |
| -0,88318162 |
| -1,4047025 |
| -0,85668363 |
| -0,96449009 |
| -0,52721546 |
| -1,4297419 |
| -1,7847328 |
| -1,906995 |
| -0,62977113 |
| -0,39857086 |
| -1,1043384 |
| -2,128906 |
| -1,9366921 |
| -2,1990534 |
| -0,28695989 |
| 1,3007485 |
| 2,1551076 |
| 1,9998826 |
| 1,8380558 |
| 2,7332339 |
| 0,39634414 |
| 0,44153691 |
| -0,00263299 |
| -0,22166991 |
| 0,59778636 |
| 1,4704076 |
| -0,0016071584 |
| -2,2409587 |
| -2,3388568 |
| -2,8305715 |
| -4,1415919 |
| -4,3279219 |
| -3,9531187 |
| -4,1364005 |
| -4,5105994 |
| -3,5049066 |
| -4,2113176 |
| -2,4074912 |
| -0,35876053 |
| 0,46224237 |
| 0,75727378 |
| -0,15464174 |
| -1,6233281 |
| -1,65949 |
| -0,44414054 |
| 1,5309014 |
| 2,0837858 |
| 2,5562922 |
| 4,2378051 |
| 6,497327 |
| 5,9536639 |
| 6,7291384 |
| 5,6114678 |
| 3,2270577 |
| 1,9529181 |
| 0,87496831 |
| 1,3245924 |
| 1,9432944 |
| 0,31389788 |
| -3,5926981 |
| -4,2868783 |
| -4,7855912 |
| -3,1697821 |
| -0,14561791 |
| 0,41649957 |
| 1,6221605 |
| 2,0590502 |
| 1,2787579 |
| 2,2069418 |
| 1,7129963 |
| 2,3512242 |
| 3,783969 |
| 1,6545973 |
| 3,2085372 |
| 4,6999246 |
| 5,5557014 |
| 4,1052794 |
| 2,3013597 |
| -0,43271732 |
| -2,9808681 |
| -4,5537181 |
| -3,8403106 |
| -0,87291545 |
| 2,1333325 |
| 2,7185373 |
| 0,28986427 |
| -0,74544557 |
| -1,8494226 |
| -3,8109461 |
| -3,5814883 |
| -2,1692477 |
| -0,17267045 |
| 0,59388903 |
| 0,44092083 |
| 0,070446436 |
| -0,30320304 |
| -0,2118101 |
| 1,5605431 |
| 2,2541393 |
| 2,800777 |
| 4,5940013 |
| 4,2325884 |
| 3,9354769 |
| 3,2937949 |
| 1,465086 |
| -2,276144 |
| -6,0704717 |
| -7,099817 |
| -6,8054636 |
| -5,7053859 |
| -5,429881 |
| -3,9790299 |
| -2,2498244 |
| -1,654975 |
| -0,26879357 |
| -1,1650796 |
| -2,4370197 |
| -2,8372476 |
| -3,7683526 |
| -2,2469797 |
| 0,45772741 |
| 1,9544737 |
| 0,90759318 |
| 0,86142529 |
| -1,8905572 |
| -3,4233825 |
| -0,30259403 |
| 1,7575166 |
| 1,2861673 |
| 1,6800238 |
| 1,2575609 |
| 1,8301534 |
| 1,3855412 |
| 2,2281142 |
| 3,2126496 |
| 3,2762618 |
| 2,3535516 |
| 1,6773353 |
| 0,81293447 |
| 0,13908669 |
| 0,47419667 |
| -0,24962781 |
| -1,362898 |
| -1,6545521 |
| -2,1962792 |
| -3,5187885 |
| -2,6059509 |
| -1,894017 |
| -2,725942 |
| -2,9913527 |
| -2,6696422 |
| -4,3091058 |
| -5,6245557 |
| -6,973058 |
| -5,1442758 |
| -3,3431442 |
| -0,66119295 |
| 1,3712853 |
| 2,5916371 |
| 2,004101 |
| 1,5944794 |
| -0,26216239 |
| -1,862031 |
| -2,9531595 |
| -2,7096487 |
| -3,8408319 |
| -5,0259297 |
| -4,4155242 |
| -1,7578889 |
| 0,28899975 |
| 0,81186867 |
| 0,86236683 |
| 0,79285108 |
| 2,5574332 |
| 2,8553897 |
| 3,3720999 |
| 2,8764269 |
| 1,2523458 |
| 0,49926024 |
| 1,0746918 |
| -0,51674198 |
| -2,2999025 |
| -2,923233 |
| -2,1868504 |
| -2,3054359 |
| -2,5532988 |
| -1,5436772 |
| -2,0652384 |
| -0,86528251 |
| 0,77107925 |
| 0,79263298 |
| 1,3048936 |
| 2,5941609 |
| 3,0345415 |
| 3,5073964 |
| 3,1710147 |
| 2,3851887 |
| Yt | Xt | dane kwartalne | ||||
| 173,087561486724 | 320,0107 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 168,620570948868 | 322,7723 | Yt | + | 1 | ||
| 164,75225534795 | 326,8495 | Xt | 3 | |||
| 182,96026652853 | 331,398824014432 | |||||
| 181,001134742137 | 334,562414962959 | |||||
| 177,989052568182 | 338,015777875707 | |||||
| 172,333893291499 | 343,16002295267 | |||||
| 191,150291070608 | 347,323900326052 | |||||
| 191,57524094477 | 352,338540981958 | |||||
| 185,194040407175 | 355,043710360558 | |||||
| 180,452512007196 | 356,253038787496 | |||||
| 198,373513931486 | 360,678435249525 | |||||
| 196,435199208244 | 365,704102109764 | |||||
| 192,133062554217 | 370,000376955072 | |||||
| 186,522960855156 | 372,73504763363 | |||||
| 206,665355036563 | 377,164873034786 | |||||
| 207,324867991556 | 380,916217463941 | |||||
| 201,093559388821 | 384,514559518056 | |||||
| 195,460386201622 | 389,668492773452 | |||||
| 213,9074311972 | 395,068522579503 | |||||
| 212,06871704391 | 399,181864180371 | |||||
| 206,572854006054 | 402,306323058384 | |||||
| 201,624404166953 | 405,832715857044 | |||||
| 223,1622374718 | 410,257828705168 | |||||
| 221,667175564491 | 415,137428009767 | |||||
| 216,355122041212 | 416,269382522816 | |||||
| 210,806825418653 | 417,408420057501 | |||||
| 229,554686204763 | 421,802357019624 | |||||
| 229,482359090881 | 428,885610486812 | |||||
| 225,591008141516 | 434,638662435556 | |||||
| 220,208731973396 | 437,162787023054 | |||||
| 239,576333499587 | 440,695128537304 | |||||
| 237,381509345183 | 446,260649459431 | |||||
| 236,09267896513 | 451,797573314794 | |||||
| 230,828659590679 | 457,614426873625 | |||||
| 248,148265132381 | 462,679084110895 | |||||
| 245,552197191465 | 466,725471305998 | |||||
| 240,938481773554 | 468,817702008641 | |||||
| 235,878646625577 | 472,146062481921 | |||||
| 255,541482911061 | 476,449150437504 | |||||
| 255,387878959146 | 480,952250225984 | |||||
| 250,213009392072 | 485,35586493799 | |||||
| 245,716804650839 | 489,621732378602 | |||||
| 265,611379337822 | 494,651820214105 | |||||
| 262,81679319319 | 498,875117155612 | |||||
| 255,853232553774 | 501,060230492164 | |||||
| 250,827142845765 | 503,795768383837 | |||||
| 270,48572532445 | 508,475591995053 | |||||
| 267,287158985457 | 511,954388643992 | |||||
| 264,444511093718 | 515,256857523975 | |||||
| 259,146627818061 | 519,411173304391 | |||||
| 279,356242404235 | 524,285243642606 | |||||
| 277,21763654124 | 529,296652499547 | |||||
| 273,221269542099 | 533,476228792731 | |||||
| 266,83450427114 | 539,081053396547 | |||||
| 287,017856377024 | 543,521735181181 | |||||
| 285,175167509203 | 547,719946231972 | |||||
| 281,937186718365 | 552,269179043514 | |||||
| 278,479154112788 | 557,857311028968 | |||||
| 298,198891247691 | 562,762683897079 | |||||
| 296,969383418052 | 568,129217536952 | |||||
| 294,26945492961 | 572,667335209645 | |||||
| 290,763883957415 | 577,146780590042 | |||||
| 309,723024936778 | 581,900156211163 | |||||
| 308,874006350381 | 587,893865869565 | |||||
| 304,578421932958 | 592,866770450317 | |||||
| 298,650887792566 | 598,734938877333 | |||||
| 320,31953980622 | 604,569661258539 | |||||
| 319,454632127643 | 609,658955078337 | |||||
| 315,885483812114 | 614,025613035753 | |||||
| 312,32970089039 | 618,189724486542 | |||||
| 331,689077838044 | 623,16731702897 | |||||
| 330,579344021714 | 629,717668719868 | |||||
| 326,708258605063 | 636,405607548346 | |||||
| 322,855595558558 | 640,347936286226 | |||||
| 341,79357626961 | 645,639725123774 | |||||
| 340,37095087756 | 651,116588047397 | |||||
| 337,356230414025 | 655,621403974189 | |||||
| 330,397147597533 | 658,961566768136 | |||||
| 348,725893003929 | 662,863821794392 | |||||
| 347,796933148337 | 667,670484189942 | |||||
| 345,14360221529 | 674,305313377214 | |||||
| 338,189254269657 | 679,29996301263 | |||||
| 359,104414459386 | 683,77875615543 | |||||
| 359,580764627167 | 689,576092872663 | |||||
| 357,163831082497 | 694,81174397416 | |||||
| 351,299646966716 | 699,340734838015 | |||||
| 371,338174688526 | 704,276069829344 | |||||
| 368,69589037666 | 708,443040979466 | |||||
| 365,283931222461 | 712,913292557996 | |||||
| 360,397407415337 | 719,093729887211 | |||||
| 381,40689519607 | 724,388447920408 | |||||
| 379,080151620593 | 728,325232005319 | |||||
| 374,991336226215 | 733,937136834497 | |||||
| 369,179871712044 | 739,071575615121 | |||||
| 389,491958489123 | 743,916633073762 | |||||
| 386,324014121537 | 748,913186290833 | |||||
| 384,415080446016 | 754,234539915912 | |||||
| 379,998402964842 | 759,524595441623 | |||||
| 402,031043499238 | 765,424981754447 |
| Zadanie |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich dwóch obserwacji) |
| dokonać wyrównania wykładniczego |
| oraz wyrównać szereg za pomocą sredniej 3-wyrazowj. |
| Obliczyć prognozy. Która metoda dała lepsze wyniki? |
| Pt |
| 17,6 |
| 17,4 |
| 16,9 |
| 17,45 |
| 15,8 |
| 15,8 |
| 15,65 |
| 15,8 |
| 15,7 |
| 16,75 |
| 16,1 |
| 16 |
| 17,1 |
| 16,45 |
| 17,7 |
| 18,05 |
| 18,35 |
| 19,05 |
| 19,75 |
| 21,8 |
| 23,5 |
| 22,9 |
| 21,4 |
| 23 |
| 26 |
| 31 |
| 35 |
| 32,1 |
| 31,2 |
| 27,6 |
| 32,2 |
| 30,6 |
| 29 |
| 28,3 |
| 28,2 |
| 28,7 |
| 28,2 |
| 28,1 |
| 29,5 |
| 29,4 |
| 29,3 |
| 28,4 |
| 26,7 |
| 27,8 |
| 22,7 |
| 22 |
| 22,5 |
| 19,3 |
| 19,95 |
| 21,9 |
| Yt | Xt | dane miesięczne | ||||
| 18,7399 | 27,0337 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 16,8152 | 25,9143 | Yt | + | 3 | ||
| 12,3805 | 25,9273 | Xt | 2 | |||
| 11,3110445923304 | 25,4861954321103 | |||||
| 26,987891830433 | 25,4475368024772 | |||||
| 28,3849831789302 | 26,891475761734 | |||||
| 31,3892479072331 | 27,4309330332138 | |||||
| 32,7411060183699 | 27,2773531232497 | |||||
| 27,0972074723659 | 27,8532471862748 | |||||
| 25,0850342108912 | 27,4799730303923 | |||||
| 28,5731913824437 | 27,6748811212746 | |||||
| 25,3840167812109 | 25,7039167848923 | |||||
| 23,8625385571101 | 26,7948417494246 | |||||
| 22,4514303542468 | 26,2345892245972 | |||||
| 18,9410175015682 | 28,105612457218 | |||||
| 16,9540802290075 | 28,0671287200526 | |||||
| 33,1391802967252 | 27,8360901040368 | |||||
| 34,0058336458606 | 28,8733630728258 | |||||
| 36,5040987303692 | 31,349354150978 | |||||
| 36,4559117021478 | 29,7733479056846 | |||||
| 28,3063726764861 | 30,1403435339792 | |||||
| 24,5061277177123 | 27,6578404737855 | |||||
| 26,0077453165893 | 27,3657883316498 | |||||
| 22,2219010245629 | 27,8514518321549 | |||||
| 20,530422279143 | 28,4382162825084 | |||||
| 20,3271207218631 | 28,1141513977559 | |||||
| 19,1675923018909 | 29,7228059784291 | |||||
| 17,9118944720457 | 29,0166641849004 | |||||
| 34,5243118906592 | 29,5097649294303 | |||||
| 33,1334986651752 | 29,6350354506012 | |||||
| 34,8995954281601 | 30,3928248154208 | |||||
| 34,4335986722297 | 30,7749773707946 | |||||
| 22,5423033403052 | 30,2651841595562 | |||||
| 20,2593034845388 | 32,1243289116893 | |||||
| 23,9535974305276 | 30,5712302381825 | |||||
| 24,7015771558372 | 32,7268611667278 | |||||
| 25,3549518440194 | 31,2328028167094 | |||||
| 28,1316797676858 | 30,0388619716966 | |||||
| 25,1806043489356 | 28,5694033801876 | |||||
| 22,1248615335587 | 28,6588823661313 | |||||
| 33,7880189959773 | 30,2073176562919 | |||||
| 29,7135591327886 | 30,4705223594044 | |||||
| 31,7296853996815 | 33,305865651583 | |||||
| 32,7787889385003 | 32,7311059561081 | |||||
| 26,0533373048509 | 32,5754741692757 | |||||
| 25,0706139471857 | 32,887531918493 | |||||
| 28,4604027539835 | 32,8323723429451 | |||||
| 27,0700136629031 | 35,1842606400616 | |||||
| 27,1469096483573 | 33,8525824480431 | |||||
| 29,2600983271673 | 34,2836077136302 | |||||
| 26,5602772704319 | 33,2037253995411 | |||||
| 25,3912021795805 | 32,3684077796788 | |||||
| 38,9884168728782 | 33,8825854457751 | |||||
| 36,8226050852393 | 32,2768098120426 | |||||
| 36,5616419859721 | 31,5528668684298 | |||||
| 36,2491069254658 | 31,8565068079009 | |||||
| 28,3538053206084 | 34,5510547655306 | |||||
| 25,6800456991208 | 35,3231383358714 | |||||
| 27,7146607233924 | 35,53929683511 | |||||
| 27,0461447035618 | 36,600507784577 | |||||
| 27,7293419473855 | 35,9918554492039 | |||||
| 27,9422604335291 | 35,8815988144427 | |||||
| 24,3978244266421 | 34,6025191701099 | |||||
| 22,893320532401 | 34,6362634190769 | |||||
| 35,9354859558285 | 36,0867843933539 | |||||
| 32,8276546117401 | 35,9821490753477 | |||||
| 35,0587959116413 | 37,4355043527434 | |||||
| 36,0898244332319 | 36,5483530469204 | |||||
| 27,5629708603142 | 35,3249471328443 | |||||
| 25,6468940479283 | 35,921762992991 | |||||
| 30,4877895653365 | 36,0368340950937 | |||||
| 31,5380766654567 | 36,9889838665656 | |||||
| 30,9106446587655 | 38,8776887065959 | |||||
| 29,6097952771001 | 38,8706820946171 | |||||
| 23,1446452258617 | 38,805077466232 | |||||
| 19,6406386947619 | 38,4701542263624 | |||||
| 31,8129566662849 | 39,2073079584537 | |||||
| 31,380486661329 | 39,7508155709176 | |||||
| 35,0259392328612 | 38,8649708996423 | |||||
| 41,5797448794558 | 41,1375796297496 | |||||
| 38,4038725690058 | 39,7121057408247 | |||||
| 39,4337389689153 | 40,2985740185773 | |||||
| 42,4597363131706 | 39,8067018130041 | |||||
| 37,6941555215571 | 40,9836912691029 | |||||
| 32,1941908973934 | 41,381283888372 | |||||
| 28,0155987877569 | 43,1865987218604 | |||||
| 20,0930945776873 | 40,5580191053023 | |||||
| 19,7245232427695 | 42,3309133737116 | |||||
| 34,4277496477285 | 43,2452393615981 | |||||
| 35,3165818233241 | 44,8192675531187 | |||||
| 38,1285435481787 | 43,4600872871831 | |||||
| 40,0563271557652 | 43,2893611010282 | |||||
| 34,7566610396332 | 44,3749527707197 | |||||
| 33,7817469718633 | 43,9964669395038 | |||||
| 37,6794688433585 | 43,6096268576527 | |||||
| 36,3292559115297 | 45,0699388003569 | |||||
| 35,6871471252079 | 45,9143571602498 | |||||
| 34,9306168180042 | 44,9136500121749 | |||||
| 31,1826727127532 | 46,0869550085224 | |||||
| 25,694633955845 | 45,5304685059657 |
| Zadanie | |
| Oblicz prognozę na okres 26, 27, 28 z najlepszego modelu średniej ruchomej (2, 3, 6- wyrazowej). | |
| Policz błedy ex post. | |
| 1 | 13170 |
| 2 | 13394 |
| 3 | 13425 |
| 4 | 27083 |
| 5 | 12402 |
| 6 | 10896 |
| 7 | 13701 |
| 8 | 25131 |
| 9 | 15715 |
| 10 | 14366 |
| 11 | 16031 |
| 12 | 27594 |
| 13 | 17977 |
| 14 | 16236 |
| 15 | 17907 |
| 16 | 28474 |
| 17 | 15567 |
| 18 | 16301 |
| 19 | 18270 |
| 20 | 31841 |
| 21 | 17972 |
| 22 | 16306 |
| 23 | 20492 |
| 24 | 33019 |
| 25 | 25583 |
| 26 | 22175 |
| 27 | 23785 |
| 28 | 34410 |
| Yt | Xt | dane miesięczne | ||||
| 53,5977 | 68,6462 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 53,3591 | 68,8497 | Yt | ||||
| 53,3382 | 69,6696 | Xt | 1 | - | 1 | |
| 54,9180017170754 | 71,3079765421383 | |||||
| 55,7506565969494 | 72,1845882710692 | |||||
| 58,7297200048835 | 72,2200941355346 | |||||
| 60,2616229015632 | 72,0187470677673 | |||||
| 60,1581297976031 | 72,5790735338836 | |||||
| 61,399610581928 | 75,5026367669418 | |||||
| 59,2123669304239 | 74,9156183834709 | |||||
| 60,0627643395833 | 76,6950091917355 | |||||
| 60,1684101260677 | 77,3129045958677 | |||||
| 61,4367172826785 | 76,9324522979339 | |||||
| 62,4110380125801 | 77,7350261489669 | |||||
| 64,0419226783008 | 79,1397130744835 | |||||
| 66,1199581610616 | 80,1699565372417 | |||||
| 66,5984373870643 | 83,1326782686209 | |||||
| 64,5434857793411 | 81,9101391343104 | |||||
| 66,3218755271235 | 80,6728695671552 | |||||
| 66,7248457754552 | 82,0908347835776 | |||||
| 66,0539184410718 | 82,8173173917888 | |||||
| 68,0109039031195 | 83,6202586958944 | |||||
| 69,1931480080306 | 83,3640293479472 | |||||
| 70,2204503705114 | 83,2679146739736 | |||||
| 69,5401962192147 | 83,9637573369868 | |||||
| 69,5379072867801 | 84,6203786684934 | |||||
| 71,3122856538275 | 86,7644893342467 | |||||
| 70,6854945633508 | 86,2389446671233 | |||||
| 73,5326666930064 | 89,0187723335617 | |||||
| 72,09082523986 | 86,7574861667808 | |||||
| 72,0372491807474 | 88,0688430833904 | |||||
| 70,7201524256032 | 87,5398215416952 | |||||
| 73,2449080731352 | 86,3387107708476 | |||||
| 75,0945452047094 | 89,5524553854238 | |||||
| 74,8211836759205 | 91,3975276927119 | |||||
| 75,2206141221996 | 90,9455638463559 | |||||
| 76,150595230641 | 91,471481923178 | |||||
| 76,7332414203036 | 93,370640961589 | |||||
| 77,9404761058235 | 93,4663204807945 | |||||
| 79,3046413078887 | 93,1961602403973 | |||||
| 80,6139257741595 | 93,9160801201986 | |||||
| 80,4870751692396 | 94,6572400600993 | |||||
| 80,3323911340456 | 96,1560200300496 | |||||
| 82,347328138757 | 96,4989100150248 | |||||
| 83,742221449822 | 96,8229550075124 | |||||
| 81,7628748625279 | 96,6852775037562 | |||||
| 80,8649423754183 | 96,9729387518781 | |||||
| 81,9236759935705 | 97,0577693759391 | |||||
| 84,6023113832264 | 99,8246846879695 | |||||
| 84,3822571397775 | 100,407742343985 | |||||
| 84,8965332290273 | 101,671571171992 | |||||
| 86,7435882966449 | 102,915785585996 | |||||
| 86,9306184621589 | 102,636392792998 | |||||
| 91,4594625779125 | 104,713296396499 | |||||
| 89,8077949062047 | 103,58954819825 | |||||
| 87,3116776464431 | 104,175074099125 | |||||
| 88,2420595116607 | 104,459137049562 | |||||
| 91,6484021604014 | 104,911568524781 | |||||
| 91,6208464880248 | 104,741684262391 | |||||
| 90,6441950676608 | 106,621342131195 | |||||
| 91,7244916472547 | 107,001171065598 | |||||
| 93,004857973565 | 105,599885532799 | |||||
| 95,4600978463691 | 107,954242766399 | |||||
| 95,7001692649201 | 108,6991213832 | |||||
| 93,2154403278403 | 108,2082606916 | |||||
| 92,8149780139921 | 108,6310303458 | |||||
| 93,3913772238943 | 110,3209151729 | |||||
| 96,6947532237472 | 110,48335758645 | |||||
| 96,7346625533743 | 110,044078793225 | |||||
| 98,9685515910176 | 110,601339396613 | |||||
| 100,76217563894 | 113,182869698306 | |||||
| 99,2288455841395 | 114,401434849153 | |||||
| 96,908314289966 | 111,625217424577 | |||||
| 98,1694830876426 | 112,771408712288 | |||||
| 99,2030561045245 | 113,073304356144 | |||||
| 99,8141278676906 | 115,211852178072 | |||||
| 100,137662980364 | 114,634226089036 | |||||
| 104,465269896574 | 116,552313044518 | |||||
| 104,253893214154 | 117,349856522259 | |||||
| 105,340195030627 | 118,99092826113 | |||||
| 106,273049105452 | 120,759864130565 | |||||
| 105,747365296403 | 120,197732065282 | |||||
| 106,28796553272 | 120,893166032641 | |||||
| 107,700191488052 | 120,314683016321 | |||||
| 109,299058695403 | 120,63794150816 | |||||
| 110,090463924989 | 120,81767075408 | |||||
| 111,840290986044 | 122,80043537704 | |||||
| 112,870414978592 | 124,73681768852 | |||||
| 109,498271519775 | 123,01170884426 | |||||
| 110,334533786995 | 123,12775442213 | |||||
| 111,206017900281 | 123,335877211065 | |||||
| 110,676327444046 | 122,958238605532 | |||||
| 114,686694265043 | 125,248319302766 | |||||
| 114,902577115074 | 125,767459651383 | |||||
| 116,879281328115 | 127,217029825692 | |||||
| 118,236380610442 | 127,608514912846 | |||||
| 116,714360159458 | 128,550557456423 | |||||
| 114,886885999142 | 129,395978728211 | |||||
| 117,387485201465 | 130,436089364106 | |||||
| 118,821386774293 | 128,651144682053 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Holta |
| b) | policzyć prognozy oraz błędy prognoz |
| Wt | |
| 17,7 | |
| 18,6 | |
| 18,8 | |
| 19,65 | |
| 19,4 | |
| 18,8 | |
| 18,55 | |
| 18,95 | |
| 19,5 | |
| 20,9 | |
| 22 | |
| 22 | |
| 21,7 | |
| 22 | |
| 20,3 | |
| 19,75 | |
| 20,8 | |
| 21,2 | |
| 21,2 | |
| 18,8 | |
| 18,55 | |
| 18 | |
| 18,65 | |
| 19,15 | |
| 18,8 | |
| 18,75 | |
| 19,4 | |
| 19,35 | |
| 19,85 | |
| 19,95 | |
| 21,2 | |
| 22,1 | |
| 21,7 | |
| 21,9 | |
| 23 | |
| 22,3 | |
| 22,1 | |
| 22,2 | |
| 22,5 | |
| 23,1 | |
| 23,8 | |
| 25,8 | |
| 25,1 | |
| 25,3 | |
| 23,7 | |
| 21,5 | |
| 23,5 | |
| 24,6 | |
| 23,9 | |
| 24,4 |
| Yt | Xt | dane kwartalne | ||||
| 377,3298 | 37,4821 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 381,4140 | 38,0932 | Yt | ||||
| 385,3879 | 37,8165 | Xt | 1 | - | 3 | |
| 387,664230454064 | 36,1601494864521 | |||||
| 390,546479579316 | 36,5819520796974 | |||||
| 393,711629898223 | 39,2179397919435 | |||||
| 395,432078677833 | 38,8255201901586 | |||||
| 396,90673917599 | 40,1229165544199 | |||||
| 400,822820701157 | 39,7894985231091 | |||||
| 402,643417552528 | 37,2749284809494 | |||||
| 406,380772757653 | 38,902405146331 | |||||
| 407,659594328891 | 38,4979832188694 | |||||
| 408,389161580863 | 39,5622574398383 | |||||
| 412,699693644325 | 38,2759890395407 | |||||
| 417,59396663828 | 37,2061150276387 | |||||
| 420,546137047959 | 37,3656007871609 | |||||
| 423,306417742816 | 38,5398036144809 | |||||
| 426,709811354236 | 39,6205642151718 | |||||
| 430,237582180246 | 38,1651047591566 | |||||
| 431,815845527937 | 38,3997333620073 | |||||
| 432,978979115354 | 39,1277747600903 | |||||
| 434,997461390835 | 38,2237108472653 | |||||
| 438,254308792568 | 37,8464985832805 | |||||
| 442,038995455189 | 39,8259411311507 | |||||
| 447,265272995776 | 38,0254690469292 | |||||
| 451,310945611313 | 38,5060049960826 | |||||
| 453,113791342136 | 40,2452495105844 | |||||
| 452,567247679381 | 40,9154921147948 | |||||
| 455,332506565311 | 38,9853229919591 | |||||
| 458,803417964393 | 40,7479314644621 | |||||
| 463,542699266659 | 42,2048741111561 | |||||
| 466,848795789717 | 41,4720348035156 | |||||
| 469,721304418505 | 40,9132379809518 | |||||
| 470,853198193938 | 39,3909595735573 | |||||
| 475,324929380143 | 37,7001193958405 | |||||
| 478,558454415635 | 38,3948074824594 | |||||
| 481,775872425763 | 39,8624790889431 | |||||
| 484,629459927279 | 40,9739732700075 | |||||
| 487,894504035785 | 40,954507077812 | |||||
| 491,149680104714 | 39,6273066679111 | |||||
| 494,303249642874 | 38,4818651978224 | |||||
| 496,735745935281 | 41,759855494318 | |||||
| 499,125812353119 | 41,6933439719627 | |||||
| 502,580331078838 | 40,9943539800542 | |||||
| 507,366726766046 | 41,4290094992965 | |||||
| 509,558523169584 | 43,0425664000949 | |||||
| 513,489531502148 | 42,2883945062599 | |||||
| 517,567313705732 | 41,5884897823348 | |||||
| 519,603264667744 | 40,7842908410749 | |||||
| 522,6722593761 | 41,8665483029815 | |||||
| 526,783146282567 | 43,2167300253371 | |||||
| 531,323290620411 | 41,4788856874554 | |||||
| 533,563294754092 | 40,7467449279773 | |||||
| 536,476323486647 | 40,3561782700217 | |||||
| 538,826772995095 | 40,8765249671066 | |||||
| 541,979902038563 | 40,4771054914316 | |||||
| 544,378598614614 | 42,300820360445 | |||||
| 549,843848059248 | 41,9574014901698 | |||||
| 553,085964822444 | 41,8201355862208 | |||||
| 555,326724248995 | 42,1796978595263 | |||||
| 557,619397763469 | 44,1985187659783 | |||||
| 559,044290328483 | 43,4460252657776 | |||||
| 561,524417812633 | 41,1881940484228 | |||||
| 566,915441062169 | 42,3014737928315 | |||||
| 571,934111572362 | 43,1825363557613 | |||||
| 576,790214734987 | 42,3803112141396 | |||||
| 579,701686981784 | 44,4026583374938 | |||||
| 584,058444950063 | 42,8113772419079 | |||||
| 585,336421651685 | 42,6201156383429 | |||||
| 587,676965758182 | 43,3235647502636 | |||||
| 590,833895981802 | 42,7436666569841 | |||||
| 594,924102031549 | 43,5660203653832 | |||||
| 597,206947717674 | 44,0044210991107 | |||||
| 602,335677588362 | 41,0324956614262 | |||||
| 603,650918055807 | 42,0867760079139 | |||||
| 608,238504081263 | 45,6129459245599 | |||||
| 613,390517716802 | 44,691144699735 | |||||
| 615,715404826758 | 43,2375293041088 | |||||
| 616,232556250521 | 44,537457496635 | |||||
| 620,177033745404 | 44,3256531473684 | |||||
| 625,512953550831 | 42,1646298707786 | |||||
| 630,277872464356 | 44,3614475034279 | |||||
| 634,187121235108 | 45,0881206696113 | |||||
| 636,020014437207 | 45,8348399909719 | |||||
| 638,566933454391 | 44,286289296191 | |||||
| 643,125744242995 | 42,1298878551071 | |||||
| 647,375769292683 | 45,3034363513799 | |||||
| 651,075212003517 | 45,916366043258 | |||||
| 654,013809885536 | 44,3944930829107 | |||||
| 657,972696078311 | 45,0091746904628 | |||||
| 662,251036177002 | 45,7154951599635 | |||||
| 666,63847986415 | 46,0084442734287 | |||||
| 669,488994327808 | 46,513264099475 | |||||
| 671,870666523137 | 46,0762713897541 | |||||
| 675,856889985422 | 45,7800181807449 | |||||
| 680,201172117454 | 43,7659786752667 | |||||
| 684,374495204109 | 45,533840293834 | |||||
| 686,728301586502 | 48,5040461511026 | |||||
| 689,730788763414 | 46,9888621073442 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | 0,448 | y2t + | 0,467 | y1t-1 + | 0,349 | y2t-1 + | 0,062 | x1t + | 0,401 | x2t + | 0,397 | x3t |
| y2t | = | -0,257 | y1t + | -0,192 | y1t-1 + | 0,107 | y2t-1 + | 0,085 | x1t + | 0,104 | x2t + | 0,169 | x3t |
| Yt | Xt | dane miesięczne | ||||
| 158,4559 | 27,7156 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 159,1349 | 26,4536 | Yt | 2 | - | 2 | |
| 162,0470 | 26,4611 | Xt | ||||
| 163,680097273553 | 29,4928102758096 | |||||
| 163,966559036053 | 30,3937942806698 | |||||
| 166,679526247519 | 26,5675037815358 | |||||
| 169,654463988706 | 28,5611252835753 | |||||
| 170,162571058701 | 30,7366578351033 | |||||
| 173,30624069621 | 28,2671263052759 | |||||
| 172,985062878411 | 27,4208782282944 | |||||
| 172,611987738185 | 29,6714449667557 | |||||
| 177,36534267344 | 29,5176397792691 | |||||
| 180,125532071494 | 28,9398980673398 | |||||
| 181,463947501958 | 29,3010562865063 | |||||
| 181,70973437152 | 29,5507810502544 | |||||
| 184,833135815715 | 30,2806751476178 | |||||
| 185,91365687426 | 30,7412470012721 | |||||
| 187,781484933359 | 30,1427524662744 | |||||
| 191,199266363032 | 30,2364619156517 | |||||
| 193,558459391725 | 29,8093084266328 | |||||
| 194,627442089924 | 28,0351352892125 | |||||
| 195,340822263674 | 28,4276539708255 | |||||
| 196,811007638218 | 31,572582686893 | |||||
| 199,582240493952 | 31,621163941352 | |||||
| 202,241329986167 | 31,019721564638 | |||||
| 200,569604070402 | 31,1158559808282 | |||||
| 202,077363698061 | 31,6554587112103 | |||||
| 206,798008956922 | 32,8057710031633 | |||||
| 211,873487321598 | 32,2526419840679 | |||||
| 213,384960721041 | 30,7439172349202 | |||||
| 212,090074513574 | 31,4373284993804 | |||||
| 214,523129535642 | 31,8369846260897 | |||||
| 218,301584041615 | 32,0235787476058 | |||||
| 220,767868928119 | 30,9840018110915 | |||||
| 222,951156852674 | 32,8686240253728 | |||||
| 224,210948315245 | 33,3755648163428 | |||||
| 225,10651628778 | 33,4098390811436 | |||||
| 225,244727752474 | 32,2141909926291 | |||||
| 228,165658401801 | 32,8114376359771 | |||||
| 231,384964062432 | 32,2328855728308 | |||||
| 234,382194107227 | 29,872261136865 | |||||
| 236,129886067943 | 31,8539263100922 | |||||
| 237,731370404628 | 33,6283692975435 | |||||
| 240,845753615825 | 32,0840220533628 | |||||
| 242,313260451424 | 31,5502832941005 | |||||
| 242,101190943319 | 32,9963805611401 | |||||
| 244,477219059851 | 33,4601716468984 | |||||
| 248,917882981472 | 31,4179111492374 | |||||
| 249,840159955529 | 32,8805890778535 | |||||
| 251,791661254982 | 33,4325966157498 | |||||
| 254,961588407881 | 32,3970441527914 | |||||
| 257,703974813418 | 33,3662564919623 | |||||
| 259,857235036891 | 34,9140086740975 | |||||
| 261,52852454778 | 33,8905353526086 | |||||
| 265,217551694856 | 33,3200628372066 | |||||
| 266,567612657273 | 32,2738662639196 | |||||
| 268,68879889613 | 31,4890347249276 | |||||
| 271,195075824999 | 31,6416665782365 | |||||
| 274,252837254622 | 32,9468294666002 | |||||
| 276,051890480875 | 32,6453387581547 | |||||
| 278,511249684541 | 34,1777199789291 | |||||
| 280,018722463705 | 33,9998522574453 | |||||
| 282,493039744799 | 32,4522926609303 | |||||
| 284,988540723529 | 32,6649053829244 | |||||
| 287,820144807998 | 36,5108448063797 | |||||
| 289,794634573547 | 34,0677248398606 | |||||
| 293,496598703079 | 31,7229175706152 | |||||
| 295,458473806201 | 33,6338185375638 | |||||
| 296,957910198985 | 34,3297971118131 | |||||
| 298,550815407807 | 34,2965567975791 | |||||
| 300,839258753255 | 33,1988472930005 | |||||
| 304,197519960126 | 32,1702313002891 | |||||
| 307,972418509022 | 33,6805496917313 | |||||
| 310,375466591306 | 35,6541199452059 | |||||
| 310,295897103137 | 35,0848293306208 | |||||
| 313,540480412011 | 36,3326056870328 | |||||
| 316,414972249013 | 34,6899174646681 | |||||
| 317,821402596224 | 35,5233511458815 | |||||
| 319,11808412719 | 35,5243863563588 | |||||
| 321,969901170574 | 35,7077326917126 | |||||
| 325,518954586175 | 34,7816473989537 | |||||
| 329,965548071345 | 34,8672164233394 | |||||
| 330,789713409623 | 36,4873388879922 | |||||
| 333,084612148331 | 34,7875001079858 | |||||
| 336,896326494775 | 34,0193416614645 | |||||
| 338,600821146312 | 35,5847544097885 | |||||
| 340,03188542872 | 37,8739992870732 | |||||
| 343,153794015536 | 36,8110417241856 | |||||
| 345,247293744668 | 35,30266778551 | |||||
| 348,03078454604 | 35,5120544543629 | |||||
| 352,236600383254 | 35,9914297909293 | |||||
| 354,194735802666 | 35,7575891371648 | |||||
| 355,329154119791 | 36,5012176084597 | |||||
| 359,583717880766 | 35,7340962604203 | |||||
| 361,539325013304 | 36,9221910490632 | |||||
| 363,716564868092 | 38,0703910631911 | |||||
| 366,926756886663 | 35,9796183626416 | |||||
| 369,49447745604 | 38,0098682359119 | |||||
| 372,014870438615 | 38,7596399982105 |
| Zadanie | |
| Dla poniższego szeregu czasowego (z pominięciem ostatnich trzech obserwacji) | |
| a) | zastosować liniowy model Wintersa |
| b) | policzyć prognozy oraz błędy prognoz |
| yt | |
| 332596 | |
| 330998 | |
| 366647 | |
| 363664 | |
| 504367 | |
| 558975 | |
| 554609 | |
| 513601 | |
| 470333 | |
| 425586 | |
| 331736 | |
| 316112 | |
| 346839 | |
| 328057 | |
| 376914 | |
| 381307 | |
| 470549 | |
| 589625 | |
| 573379 | |
| 481027 | |
| 444179 | |
| 419558 | |
| 325963 | |
| 303565 | |
| 336469 | |
| 319614 | |
| 369843 | |
| 391803 | |
| 475097 | |
| 595903 | |
| 591491 | |
| 559410 | |
| 523380 | |
| 463932 | |
| 351063 | |
| 331086 | |
| 353070 | |
| 339084 | |
| 381429 | |
| 393236 | |
| 522463 | |
| 611667 | |
| 597763 | |
| 525054 | |
| 507200 | |
| 470763 | |
| 375066 | |
| 379495 | |
| 410678 | |
| 407783 | |
| 457506 | |
| 473943 | |
| 637559 | |
| 726153 | |
| 682582 | |
| 654554 | |
| 638730 | |
| 599457 | |
| 469232 | |
| 441060 | |
| 475435 | |
| 449198 | |
| 520786 | |
| 518934 | |
| 697969 | |
| 804968 | |
| 775588 | |
| 742621 | |
| 709088 | |
| 637739 | |
| 513214 | |
| 512842 | |
| 563484 | |
| 526395 | |
| 595654 | |
| 593429 | |
| 750967 | |
| 909751 | |
| 887626 | |
| 806736 | |
| 758042 | |
| 659707 | |
| 514318 | |
| 485064 | |
| 513733 | |
| 480235 | |
| 554126 | |
| 579897 | |
| 781771 | |
| 905767 | |
| 878118 | |
| 826922 | |
| 783158 | |
| 701655 | |
| 539899 | |
| 547867 |
| Yt | Xt | dane kwartalne | ||||
| 39,2279 | 17,6484 | Struktura | st. w. trendu | sezonow | rząd AR | |
| 37,9533 | 19,8520 | Yt | - | 2 | ||
| 38,2954 | 17,9904 | Xt | 1 | |||
| 38,7228788859955 | 17,8092220564476 | |||||
| 39,4279548879703 | 19,5383744983419 | |||||
| 42,1341560557961 | 18,4426624893655 | |||||
| 43,0497618056394 | 19,6174970575331 | |||||
| 42,7000063136456 | 19,977874975872 | |||||
| 42,9923776242412 | 21,628833370962 | |||||
| 43,4323800021062 | 20,8398702671298 | |||||
| 44,6780200957983 | 19,4041730907377 | |||||
| 43,532216240085 | 19,8572748303485 | |||||
| 45,4131944264456 | 20,7128320583441 | |||||
| 46,2360710219307 | 21,2755849923806 | |||||
| 48,8497606078946 | 21,2952393455187 | |||||
| 49,3216525476038 | 21,2867866521621 | |||||
| 48,8233505648854 | 22,0831598556853 | |||||
| 50,2114704072531 | 22,3700758157292 | |||||
| 53,6891103878267 | 21,9759397000185 | |||||
| 52,2629677472535 | 23,1360851064257 | |||||
| 52,7081380708489 | 21,1912672957106 | |||||
| 51,2736271453071 | 20,5736693263602 | |||||
| 52,2164190817279 | 21,6917045631161 | |||||
| 54,9270446950829 | 21,6343344864805 | |||||
| 57,0795516995011 | 21,3404562909294 | |||||
| 57,2028565210504 | 21,4428230830508 | |||||
| 58,930823650874 | 21,7743592432376 | |||||
| 58,9334312385356 | 21,2855880305657 | |||||
| 60,0751726958076 | 20,2698920558652 | |||||
| 60,9709806739641 | 21,3674522618239 | |||||
| 62,4819760541885 | 22,3417308940831 | |||||
| 63,7835778712197 | 21,7291350902591 | |||||
| 63,7007889963122 | 22,1721252202435 | |||||
| 66,3369353205407 | 21,5606557398363 | |||||
| 65,9927039153778 | 20,4092517479133 | |||||
| 68,0241601673205 | 23,6247290212631 | |||||
| 67,64137243054 | 23,6463472320985 | |||||
| 67,4506086303379 | 21,3651705360431 | |||||
| 67,162086921936 | 22,4852098490403 | |||||
| 69,1124397949832 | 23,4944022252229 | |||||
| 72,7885141788019 | 23,2386320425857 | |||||
| 74,2933214325252 | 22,3314741192755 | |||||
| 76,6367174229048 | 24,7802804799791 | |||||
| 76,358798335843 | 23,4550963647261 | |||||
| 76,1901913125623 | 22,5064492257518 | |||||
| 77,5866002757366 | 21,9503068768787 | |||||
| 78,9772830763881 | 22,5511072559712 | |||||
| 82,8441899192094 | 21,5212406844752 | |||||
| 81,9320159281549 | 23,5832254723745 | |||||
| 82,4762335041758 | 23,3269394348015 | |||||
| 82,9997971718091 | 20,7895562691033 | |||||
| 83,0353193445883 | 23,8272857716758 | |||||
| 86,0320154661222 | 25,8253353148996 | |||||
| 86,3641069882364 | 24,3691596482778 | |||||
| 86,394066255259 | 24,2198204191764 | |||||
| 88,0320731690664 | 24,7103473361671 | |||||
| 92,2811284984683 | 25,8332247383695 | |||||
| 94,4845370574988 | 23,9843497783329 | |||||
| 94,1674264380312 | 25,3320419570557 | |||||
| 95,201246733 | 25,7724567969963 | |||||
| 95,9853609061929 | 23,4652400873484 | |||||
| 96,9261766397876 | 24,0143673872516 | |||||
| 96,7745532432586 | 26,2595662880954 | |||||
| 98,656806990325 | 25,3147643165323 | |||||
| 102,099627448301 | 24,7902093176346 | |||||
| 103,522444107701 | 23,8132676897132 | |||||
| 105,210191433875 | 25,1639971439014 | |||||
| 104,611963376501 | 27,2414604141735 | |||||
| 104,703769218451 | 24,5364385604416 | |||||
| 106,666104628848 | 26,2786367287049 | |||||
| 109,308033371301 | 24,6962152061842 | |||||
| 111,613676502497 | 25,2307827759505 | |||||
| 114,167874090744 | 26,5475758942659 | |||||
| 114,187632625452 | 28,860838566158 | |||||
| 114,616120652697 | 27,6970192133735 | |||||
| 115,459740302878 | 27,1662712943552 | |||||
| 118,050632845509 | 26,4407704669616 | |||||
| 120,00442821041 | 28,2617306411528 | |||||
| 120,604866752575 | 26,6204153752437 | |||||
| 124,264279950889 | 24,637401051144 | |||||
| 123,648379778398 | 27,589481936115 | |||||
| 125,443290528095 | 25,6843555341516 | |||||
| 126,225470946096 | 27,3440778430549 | |||||
| 128,958983082014 | 27,6276208641995 | |||||
| 131,162730527111 | 26,4897960995936 | |||||
| 133,427481396439 | 29,0591477491886 | |||||
| 131,688041780426 | 28,6283444426372 | |||||
| 135,118371488418 | 24,497152672217 | |||||
| 137,899739488949 | 26,4502872859334 | |||||
| 140,488889758289 | 28,5523380012357 | |||||
| 140,161639726836 | 26,6782795491577 | |||||
| 140,82420086329 | 25,293667876479 | |||||
| 143,262372231266 | 27,8793508860914 | |||||
| 144,680052489391 | 29,4235959013244 | |||||
| 146,1082727044 | 27,2119666699981 | |||||
| 149,013775340213 | 27,1545780748202 | |||||
| 151,146896075908 | 28,6602604091935 | |||||
| 151,235347697531 | 28,163724075231 | |||||
| 153,769350819988 | 26,3916271222984 | |||||
| 154,8910916 | 26,9243857081888 |
| Zadanie | |||||||||||||
| Wyznaczyć mnożnik bezpośredni i mnożniki pośrednie (do 4 rzędu) oraz podać ich interpretację ekonomiczną. | |||||||||||||
| y1t | = | 0,166 | y2t + | -0,232 | y1t-1 + | 0,234 | y2t-1 + | 0,493 | y3t-1 + | -0,354 | x1t + | -0,085 | x2t |
| y2t | = | -0,072 | y3t + | 0,243 | y1t-1 + | -0,209 | y2t-1 + | 0,461 | y3t-1 + | -0,359 | x1t + | -0,007 | x2t |
| y3t | = | 0,048 | y1t + | -0,375 | y1t-1 + | 0,311 | y2t-1 + | 0,189 | y3t-1 + | 0,427 | x1t + | 0,435 | x2t |