Zadanie 1. |
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Przyjmujemy: {prz x(t)}~AR(1) |
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Sprawdzić występowanie pierwiastka jednostkowego równego jeden dla procesu {xt}, |
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prz x(t)= stała + gamma1*prz x(t-1) + epsilon(t) |
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Najpierw, co już zostało zrobione, należy inaczej zdefiniować inflację. Pierwszy rodzaj to prosta stopa zwrotu czyli =inf-100*(inf-100)/100. Ale tak nie robimy, przechodzimy na logarytmy, bo przekształcają one na całą oś rzeczywistą. I teraz inflacja to przyrost rzeczywistego poziomu cen. |
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traktując szereg czasowy jako jego realizację. |
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H0:delta1=0 |
<---- pierwiastek jednostkowy występuje |
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Zastosować test Dickeya i Fullera |
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H1:delta1<0 |
<------ jest kow. Stacjonarny |
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GUS=100*CPI(t)/CPI(t-12) |
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to podaje GUS, ale to naprawdę nie jest inflacja |
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Reparametryzacja: |
prz x(t) - prz x(t-1) =stała+ *gamma1-1)*prz x(t-1) + epsilon(t) |
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x(t) ---> |
inflacja=100*[ln(CPI(t))-ln(CPI(t-12))] |
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tak jest w artykułach naukowych |
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Regresja Dickeya i Fullera: |
prz2 x(t) =stała+ * gamma1 *prz x(t-1) + epsilon(t) |
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GUS |
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r/r |
inflacja |
przy x(t) |
x(t-1) |
przy x(t-1) |
prz2 x(t) |
reszty e |
przyrosty reszty |
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delta=gamma1-1 |
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rok |
miesiąc |
inflacja GUS |
100*ln( GUS/100 ) |
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gamma1^ |
stała^ |
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2002 |
1 |
103,4 |
3,34347760862374 |
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0,68801192438476 |
0,003240178673997 |
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2 |
103,5 |
3,44014267173323 |
0,09666506310949 |
3,34347760862374 |
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0,082547780669746 |
0,031306995877186 |
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3 |
103,3 |
3,24671901375014 |
-0,19342365798309 |
3,44014267173323 |
0,09666506310949 |
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0,350019240571685 |
0,358101464887822 |
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4 |
103 |
2,95588022415444 |
-0,290838789595698 |
3,24671901375014 |
-0,19342365798309 |
-0,29008872109258 |
-0,160251116616091 |
-0,160251116616091 |
69,4674132715264 |
129 |
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5 |
101,9 |
1,88217542405879 |
-1,07370480009565 |
2,95588022415444 |
-0,290838789595698 |
-0,097415131612608 |
0,099445245028866 |
0,259696361644957 |
8,90826899806665 |
16,5425290309697 |
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Oznacza że w tym modelu jest zbyt mało opóźnień bo DW jest zamałe. Założenie o niezależności epsilon(t) nie jest spełnione |
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6 |
101,6 |
1,58733491562902 |
-0,294840508429772 |
1,88217542405879 |
-1,07370480009565 |
-0,782866010499956 |
-0,047384483438989 |
-0,146829728467854 |
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#DIV/0! |
1,97852449147927 |
nieformalnie |
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7 |
101,3 |
1,29162252665462 |
-0,295712388974394 |
1,58733491562902 |
-0,294840508429772 |
0,778864291665882 |
0,978477898583233 |
1,02586238202222 |
ADF= |
0,103496952780396 |
powinno być -8,10265 |
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8 |
101,2 |
1,19285708652738 |
-0,098765440127242 |
1,29162252665462 |
-0,295712388974394 |
-0,000871880544621 |
0,199341590584069 |
-0,779136307999165 |
POZ.IST= |
0,05 |
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9 |
101,3 |
1,29162252665462 |
0,098765440127242 |
1,19285708652738 |
-0,098765440127242 |
0,196946948847152 |
0,261658570697806 |
0,062316980113738 |
ASYPT.W.KRYT= |
-1,941 |
bez stałej |
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10 |
101,1 |
1,09399400383343 |
-0,197628522821196 |
1,29162252665462 |
0,098765440127242 |
0,197530880254483 |
0,126338901055835 |
-0,135319669641971 |
ASYPT.W.KRYT= |
-2,861 |
model ze stałą |
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11 |
100,9 |
0,895974137147202 |
-0,198019866686224 |
1,09399400383343 |
-0,197628522821196 |
-0,296393962948438 |
-0,163663361322906 |
-0,290002262378741 |
KONK= |
brak podstaw do odrzucenia H0 |
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12 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
-0,198019866686224 |
-0,000391343865028 |
0,132608507006178 |
0,296271868329084 |
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2003 |
1 |
100,5 |
0,498754151103897 |
-0,298062813813791 |
0,796816964917688 |
-0,099157172229514 |
0,09886269445671 |
0,163843832664892 |
0,031235325658714 |
UWAGA Patrz na DW |
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2 |
100,5 |
0,498754151103897 |
0 |
0,498754151103897 |
-0,298062813813791 |
-0,198905641584277 |
0,002924949861288 |
-0,160918882803604 |
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3 |
100,6 |
0,598207167754747 |
0,09945301665085 |
0,498754151103897 |
0 |
0,298062813813791 |
0,294822635139794 |
0,291897685278506 |
DW= |
2,01868054391261 |
chceby by DW=~2 |
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4 |
100,3 |
0,299550897979837 |
-0,29865626977491 |
0,598207167754747 |
0,09945301665085 |
0,09945301665085 |
0,027787976605032 |
-0,267034658534762 |
ro^= |
-0,009340271956303 |
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5 |
100,4 |
0,399202126953746 |
0,099651228973909 |
0,299550897979837 |
-0,29865626977491 |
-0,39810928642576 |
-0,195870390202347 |
-0,22365836680738 |
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6 |
100,8 |
0,796816964917688 |
0,397614837963942 |
0,399202126953746 |
0,099651228973909 |
0,398307498748818 |
0,326506086261176 |
0,522376476463524 |
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7 |
100,8 |
0,796816964917688 |
0 |
0,796816964917688 |
0,397614837963942 |
0,297963608990034 |
0,02115968048453 |
-0,305346405776646 |
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8 |
100,7 |
0,697561373642536 |
-0,099255591275152 |
0,796816964917688 |
0 |
-0,397614837963942 |
-0,40085501663794 |
-0,42201469712247 |
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9 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
-0,099255591275152 |
-0,099255591275152 |
-0,034206739589985 |
0,366648277047955 |
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10 |
101,3 |
1,29162252665462 |
0,395648389507421 |
0,895974137147202 |
0,198412763504666 |
0,297668354779819 |
0,157917828864478 |
0,192124568454463 |
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11 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
0,395648389507421 |
0,197235626002754 |
-0,078215362515974 |
-0,236133191380452 |
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12 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0,295712388974394 |
-0,099936000533027 |
-0,306629829009711 |
-0,228414466493737 |
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2004 |
1 |
101,6 |
1,58733491562902 |
-0,098376791013286 |
1,6857117066423 |
0,098376791013286 |
-0,197335597961108 |
-0,268260181934953 |
0,038369647074758 |
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2 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
-0,098376791013286 |
-0,196753582026572 |
-0,132309355400721 |
0,135950826534232 |
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3 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0 |
0,098376791013286 |
0,095136612339289 |
0,22744596774001 |
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4 |
102,2 |
2,17614917815127 |
0,490437471508969 |
1,6857117066423 |
0,098376791013286 |
0,098376791013286 |
0,027452207039441 |
-0,067684405299848 |
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5 |
103,4 |
3,34347760862374 |
1,16732843047247 |
2,17614917815127 |
0,490437471508969 |
0,392060680495683 |
0,051393673258404 |
0,023941466218964 |
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6 |
104,4 |
4,3059489460447 |
0,962471337420959 |
3,34347760862374 |
1,16732843047247 |
0,676890958963502 |
-0,129485099548901 |
-0,180878772807305 |
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7 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,962471337420959 |
-0,204857093051512 |
-0,870289028749676 |
-0,740803929200776 |
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8 |
104,6 |
4,49733656427312 |
0 |
4,49733656427312 |
0,191387618228418 |
-0,771083719192541 |
-0,906000861387288 |
-0,035711832637611 |
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9 |
104,4 |
4,3059489460447 |
-0,191387618228418 |
4,49733656427312 |
0 |
-0,191387618228418 |
-0,194627796902416 |
0,711373064484872 |
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10 |
104,5 |
4,40168854167743 |
0,095739595632725 |
4,3059489460447 |
-0,191387618228418 |
-0,191387618228418 |
-0,062950833381666 |
0,13167696352075 |
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11 |
104,5 |
4,40168854167743 |
0 |
4,40168854167743 |
0,095739595632725 |
0,287127213861143 |
0,218017051756056 |
0,280967885137722 |
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12 |
104,4 |
4,3059489460447 |
-0,095739595632725 |
4,40168854167743 |
0 |
-0,095739595632725 |
-0,098979774306722 |
-0,316996826062778 |
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2005 |
1 |
103,7 |
3,63319292473902 |
-0,67275602130568 |
4,3059489460447 |
-0,095739595632725 |
-0,095739595632725 |
-0,033109790875632 |
0,06586998343109 |
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2 |
103,6 |
3,53671438372913 |
-0,096478541009886 |
3,63319292473902 |
-0,67275602130568 |
-0,577016425672956 |
-0,117392439486998 |
-0,084282648611366 |
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3 |
103,4 |
3,34347760862374 |
-0,193236775105393 |
3,53671438372913 |
-0,096478541009886 |
0,576277480295794 |
0,639415688283843 |
0,756808127770841 |
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4 |
103 |
2,95588022415444 |
-0,387597384469299 |
3,34347760862374 |
-0,193236775105393 |
-0,096758234095507 |
0,032950792732663 |
-0,60646489555118 |
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5 |
102,5 |
2,46926125903714 |
-0,486618965117302 |
2,95588022415444 |
-0,387597384469299 |
-0,194360609363907 |
0,069070834337318 |
0,036120041604656 |
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6 |
101,4 |
1,39029051689914 |
-1,078970742138 |
2,46926125903714 |
-0,486618965117302 |
-0,099021580648003 |
0,232537891310475 |
0,163467056973157 |
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7 |
101,3 |
1,29162252665462 |
-0,098667990244521 |
1,39029051689914 |
-1,078970742138 |
-0,592351777020697 |
0,146752780958523 |
-0,085785110351953 |
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8 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
-0,098667990244521 |
0,980302751893478 |
1,04494732706279 |
0,898194546104267 |
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9 |
101,8 |
1,7839918128331 |
0,196656897204085 |
1,58733491562902 |
0,295712388974394 |
0,394380379218914 |
0,18768655074223 |
-0,85726077632056 |
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10 |
101,6 |
1,58733491562902 |
-0,196656897204085 |
1,7839918128331 |
0,196656897204085 |
-0,099055491770308 |
-0,237597960733224 |
-0,425284511475454 |
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11 |
101 |
0,995033085316809 |
-0,592301830312207 |
1,58733491562902 |
-0,196656897204085 |
-0,39331379440817 |
-0,261251682793249 |
-0,023653722060025 |
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12 |
100,7 |
0,697561373642536 |
-0,297471711674273 |
0,995033085316809 |
-0,592301830312207 |
-0,395644933108122 |
0,008625610307598 |
0,269877293100847 |
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2006 |
1 |
100,6 |
0,598207167754747 |
-0,099354205887789 |
0,697561373642536 |
-0,297471711674273 |
0,294830118637934 |
0,496254024762982 |
0,487628414455384 |
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2 |
100,7 |
0,697561373642536 |
0,099354205887789 |
0,598207167754747 |
-0,099354205887789 |
0,198117505786484 |
0,263234205501064 |
-0,233019819261917 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
100,4 |
0,399202126953746 |
-0,29835924668879 |
0,697561373642536 |
0,099354205887789 |
0,198708411775578 |
0,127111354713004 |
-0,136122850788061 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
100,7 |
0,697561373642536 |
0,29835924668879 |
0,399202126953746 |
-0,29835924668879 |
-0,397713452576579 |
-0,195678911778235 |
-0,322790266491238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
0,29835924668879 |
0,59671849337758 |
0,388203595231241 |
0,583882507009476 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
0,198412763504666 |
-0,099946483184124 |
-0,239697009099465 |
-0,627900604330706 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
101,1 |
1,09399400383343 |
0,297177038915738 |
0,796816964917688 |
-0,099157172229514 |
-0,29756993573418 |
-0,232588797525998 |
0,007108211573466 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,6 |
1,58733491562902 |
0,49334091179559 |
1,09399400383343 |
0,297177038915738 |
0,396334211145252 |
0,188632686043873 |
0,421221483569872 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
0,49334091179559 |
0,196163872879852 |
-0,146500735896361 |
-0,335133421940235 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
101,2 |
1,19285708652738 |
-0,394477829101635 |
1,58733491562902 |
0 |
-0,49334091179559 |
-0,496581090469587 |
-0,350080354573226 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
101,4 |
1,39029051689914 |
0,197433430371762 |
1,19285708652738 |
-0,394477829101635 |
-0,394477829101635 |
-0,126312557448294 |
0,370268533021293 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
101,4 |
1,39029051689914 |
0 |
1,39029051689914 |
0,197433430371762 |
0,591911259473397 |
0,45283452643144 |
0,579147083879733 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2007 |
1 |
101,6 |
1,58733491562902 |
0,197044398729873 |
1,39029051689914 |
0 |
-0,197433430371762 |
-0,200673609045759 |
-0,653508135477199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
101,9 |
1,88217542405879 |
0,294840508429772 |
1,58733491562902 |
0,197044398729873 |
0,197044398729873 |
0,058235324096498 |
0,258908933142257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
102,5 |
2,46926125903714 |
0,587085834978353 |
1,88217542405879 |
0,294840508429772 |
0,097796109699899 |
-0,108297854565447 |
-0,166533178661945 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,3 |
2,27394869694893 |
-0,195312562088207 |
2,46926125903714 |
0,587085834978353 |
0,29224532654858 |
-0,114916907227907 |
-0,00661905266246 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,3 |
2,27394869694893 |
0 |
2,27394869694893 |
-0,195312562088207 |
-0,78239839706656 |
-0,651261204041732 |
-0,536344296813825 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
102,6 |
2,56677467485778 |
0,292825977908847 |
2,27394869694893 |
0 |
0,195312562088207 |
0,19207238341421 |
0,843333587455942 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
102,3 |
2,27394869694893 |
-0,292825977908847 |
2,56677467485778 |
0,292825977908847 |
0,292825977908847 |
0,088118034663935 |
-0,103954348750275 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,5 |
1,48886124937506 |
-0,785087447573878 |
2,27394869694893 |
-0,292825977908847 |
-0,585651955817695 |
-0,387424369920777 |
-0,475542404584712 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
102,3 |
2,27394869694893 |
0,785087447573878 |
1,48886124937506 |
-0,785087447573878 |
-0,492261469665031 |
0,044647877276595 |
0,432072247197372 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103 |
2,95588022415444 |
0,681931527205509 |
2,27394869694893 |
0,785087447573878 |
1,57017489514776 |
1,02678519085814 |
0,982137313581541 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,6 |
3,53671438372913 |
0,580834159574692 |
2,95588022415444 |
0,681931527205509 |
-0,103155920368369 |
-0,575573121373666 |
-1,6023583122318 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,580834159574692 |
-0,101097367630818 |
-0,503958374182203 |
0,071614747191464 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2008 |
1 |
104 |
3,92207131532813 |
0 |
3,92207131532813 |
0,385356931598998 |
-0,195477227975693 |
-0,463847570734123 |
0,040110803448079 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
104,2 |
4,11419433311752 |
0,192123017789389 |
3,92207131532813 |
0 |
-0,385356931598998 |
-0,388597110272995 |
0,075250460461128 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
0,192123017789389 |
0,192123017789389 |
0,056699911927507 |
0,445297022200502 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
-0,096107647955044 |
4,01817896328318 |
-0,096015369834345 |
-0,288138387623734 |
-0,225318846927489 |
-0,282018758854996 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
104,4 |
4,3059489460447 |
0,383877630716568 |
3,92207131532813 |
-0,096107647955044 |
-9,22781206988965E-05 |
0,062790751022947 |
0,288109597950435 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,383877630716568 |
0,479985278671612 |
0,212632712560047 |
0,1498419615371 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104,8 |
4,68835858988505 |
0,191022025611926 |
4,49733656427312 |
0,191387618228418 |
-0,19249001248815 |
-0,327407154682897 |
-0,540039867242944 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,8 |
4,68835858988505 |
0 |
4,68835858988505 |
0,191022025611926 |
-0,000365592616492 |
-0,135031202731626 |
0,192375951951271 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
104,5 |
4,40168854167743 |
-0,28667004820762 |
4,68835858988505 |
0 |
-0,191022025611926 |
-0,194262204285923 |
-0,059231001554298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,2 |
4,11419433311752 |
-0,287494208559904 |
4,40168854167743 |
-0,28667004820762 |
-0,28667004820762 |
-0,092677815350821 |
0,101584388935103 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,7 |
3,63319292473902 |
-0,481001408378501 |
4,11419433311752 |
-0,287494208559904 |
-0,000824160352284 |
0,193735104654492 |
0,286412920005313 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,3 |
3,24671901375014 |
-0,38647391098888 |
3,63319292473902 |
-0,481001408378501 |
-0,193507199818597 |
0,134187326117678 |
-0,059547778536814 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2009 |
1 |
102,8 |
2,76151670329734 |
-0,485202310452802 |
3,24671901375014 |
-0,38647391098888 |
0,094527497389621 |
0,357185977939587 |
0,222998651821909 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,3 |
3,24671901375014 |
0,485202310452802 |
2,76151670329734 |
-0,485202310452802 |
-0,098728399463923 |
0,231856397192644 |
-0,125329580746943 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
103,6 |
3,53671438372913 |
0,289995369978993 |
3,24671901375014 |
0,485202310452802 |
0,970404620905605 |
0,633339466901043 |
0,401483069708399 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,289995369978993 |
-0,195206940473809 |
-0,397967391709724 |
-1,03130685861077 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
0,385356931598998 |
0,095361561620005 |
-0,173008781138425 |
0,224958610571298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
103,5 |
3,44014267173323 |
-0,096571711995903 |
3,53671438372913 |
-0,385356931598998 |
-0,770713863197996 |
-0,508823877787561 |
-0,335815096649135 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
103,6 |
3,53671438372913 |
0,096571711995903 |
3,44014267173323 |
-0,096571711995903 |
0,288785219603095 |
0,35198753034053 |
0,860811408128091 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
103,7 |
3,63319292473902 |
0,096478541009886 |
3,53671438372913 |
0,096571711995903 |
0,193143423991806 |
0,123460755906377 |
-0,228526774434153 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
103,4 |
3,34347760862374 |
-0,289715316115279 |
3,63319292473902 |
0,096478541009886 |
-9,31709860170216E-05 |
-0,06971173632206 |
-0,193172492228437 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103,1 |
3,05292050348228 |
-0,290557105141463 |
3,34347760862374 |
-0,289715316115279 |
-0,386193857125165 |
-0,19010644363495 |
-0,12039470731289 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,3 |
3,24671901375014 |
0,193798510267862 |
3,05292050348228 |
-0,290557105141463 |
-0,000841789026184 |
0,195824785351861 |
0,385931228986811 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,5 |
3,44014267173323 |
0,19342365798309 |
3,24671901375014 |
0,193798510267862 |
0,484355615409325 |
0,347779750743036 |
0,151954965391175 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
103,6 |
1 |
103,5 |
3,44014267173323 |
0 |
3,44014267173323 |
0,19342365798309 |
-0,000374852284772 |
-0,136692814109254 |
-0,484472564852291 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
102,9 |
2,85874568519127 |
-0,581396986541963 |
3,44014267173323 |
0 |
-0,19342365798309 |
-0,196663836657087 |
-0,059971022547833 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
102,6 |
2,56677467485778 |
-0,291971010333487 |
2,85874568519127 |
-0,581396986541963 |
-0,581396986541963 |
-0,184629105673724 |
0,012034730983364 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,4 |
2,37165266173161 |
-0,195122013126175 |
2,56677467485778 |
-0,291971010333487 |
0,289425976208476 |
0,487065334218584 |
0,671694439892308 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,2 |
2,17614917815127 |
-0,195503483580335 |
2,37165266173161 |
-0,195122013126175 |
0,096848997207312 |
0,227855090274083 |
-0,259210243944501 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
102,3 |
2,27394869694893 |
0,097799518797663 |
2,17614917815127 |
-0,195503483580335 |
-0,00038147045416 |
0,130887078833873 |
-0,09696801144021 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
102 |
1,98026272961797 |
-0,293685967330961 |
2,27394869694893 |
0,097799518797663 |
0,293303002377998 |
0,222775588572117 |
0,091888509738244 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
102 |
1,98026272961797 |
0 |
1,98026272961797 |
-0,293685967330961 |
-0,391485486128624 |
-0,192666217254447 |
-0,415441805826564 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
102,5 |
2,46926125903714 |
0,488998529419169 |
1,98026272961797 |
0 |
0,293685967330961 |
0,290445788656964 |
0,483112005911411 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
102,8 |
2,76151670329734 |
0,292255444260197 |
2,46926125903714 |
0,488998529419169 |
0,488998529419169 |
0,149321531498172 |
-0,141124257158792 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
102,7 |
2,66419309464213 |
-0,097323608655208 |
2,76151670329734 |
0,292255444260197 |
-0,196743085158971 |
-0,40105849445035 |
-0,550380025948521 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,1 |
3,05292050348228 |
0,388727408840148 |
2,66419309464213 |
-0,097323608655208 |
-0,389579052915405 |
-0,325859428310464 |
0,075199066139886 |
|
|
|
|
|
|
|
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2011 |
1 |
103,8 |
3,72957847436969 |
0,676657970887414 |
3,05292050348228 |
0,388727408840148 |
0,486051017495356 |
0,215361746204147 |
0,541221174514611 |
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2 |
103,6 |
3,53671438372913 |
-0,192864090640558 |
3,72957847436969 |
0,676657970887414 |
0,287930562047265 |
-0,180858369327268 |
-0,396220115531415 |
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3 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
-0,192864090640558 |
-0,869522061527972 |
-0,740069446055642 |
-0,559211076728374 |
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4 |
104,5 |
4,40168854167743 |
0,191570939813893 |
4,21011760186353 |
0,673403218134398 |
0,866267308774956 |
0,399717686105422 |
1,13978713216106 |
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5 |
105 |
4,87901641694321 |
0,47732787526578 |
4,40168854167743 |
0,191570939813893 |
-0,481832278320505 |
-0,616875547952056 |
-1,01659323405748 |
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6 |
104,2 |
4,11419433311752 |
-0,764822083825684 |
4,87901641694321 |
0,47732787526578 |
0,285756935451887 |
-0,045890513246208 |
0,570985034705848 |
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7 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
-0,764822083825684 |
-1,24214995909146 |
-0,71918342406059 |
-0,673292910814382 |
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8 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
-0,096015369834345 |
0,668806713991339 |
0,731626254687584 |
1,45080967874817 |
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9 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
0,191938638580356 |
0,287954008414701 |
0,152657757647242 |
-0,578968497040342 |
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10 |
104,3 |
4,21011760186353 |
0,384246390154484 |
3,82587121170905 |
-0,384246390154484 |
-0,57618502873484 |
-0,315059109080754 |
-0,467716866727996 |
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11 |
104,8 |
4,68835858988505 |
0,478240988021513 |
4,21011760186353 |
0,384246390154484 |
0,768492780308969 |
0,500886503306888 |
0,815945612387641 |
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12 |
104,6 |
4,49733656427312 |
-0,191022025611926 |
4,68835858988505 |
0,478240988021513 |
0,093994597867029 |
-0,238281083295318 |
-0,739167586602206 |
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2012 |
1 |
104,1 |
4,01817896328318 |
-0,479157600989943 |
4,49733656427312 |
-0,191022025611926 |
-0,669263013633439 |
-0,5410777608663 |
-0,302796677570982 |
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2 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
-0,479157600989943 |
-0,288135575378017 |
0,038290389088662 |
0,579368149954962 |
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3 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
0,191938638580356 |
0,671096239570299 |
0,53579998880284 |
0,497509599714179 |
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4 |
104 |
3,92207131532813 |
0,096200103619085 |
3,82587121170905 |
-0,384246390154484 |
-0,57618502873484 |
-0,315059109080754 |
-0,850859097883594 |
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5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
0,096200103619085 |
0,480446493773569 |
0,411019496682592 |
0,726078605763346 |
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6 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
-0,385356931598998 |
-0,481557035218083 |
-0,219667049807647 |
-0,630686546490239 |
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7 |
104 |
3,92207131532813 |
-0,2880462865354 |
4,21011760186353 |
0,673403218134398 |
1,0587601497334 |
0,592210527063862 |
0,811877576871509 |
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8 |
103,8 |
3,72957847436969 |
-0,19249284095844 |
3,92207131532813 |
-0,2880462865354 |
-0,961449504669798 |
-0,766510403432691 |
-1,35872093049655 |
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9 |
103,8 |
3,72957847436969 |
0 |
3,72957847436969 |
-0,19249284095844 |
0,09555344557696 |
0,224750636841068 |
0,991261040273759 |
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10 |
103,4 |
3,34347760862374 |
-0,386100865745951 |
3,72957847436969 |
0 |
0,19249284095844 |
0,189252662284443 |
-0,035497974556626 |
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11 |
102,8 |
2,76151670329734 |
-0,581960905326403 |
3,34347760862374 |
-0,386100865745951 |
-0,386100865745951 |
-0,123699044771455 |
-0,312951707055897 |
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12 |
102,4 |
2,37165266173161 |
-0,389864041565732 |
2,76151670329734 |
-0,581960905326403 |
-0,195860039580452 |
0,201295824135866 |
0,324994868907321 |
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2013 |
1 |
101,7 |
1,6857117066423 |
-0,685940955089304 |
2,37165266173161 |
-0,389864041565732 |
0,192096863760671 |
0,457087794572733 |
0,255791970436867 |
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2 |
101,3 |
1,29162252665462 |
-0,39408917998768 |
1,6857117066423 |
-0,685940955089304 |
-0,296076913523572 |
0,172618464327743 |
-0,28446933024499 |
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Zadanie 1. |
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Przyjmujemy: {x(t)}~AR(2) |
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Sprawdzić występowanie pierwiastka jednostkowego równego jeden dla procesu {xt}, |
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x(t)=fi_1*x(t-1) + fi_2*x(t-2) + epsilon(t), {epsilon}~iiN(0,sigma2) |
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Najpierw, co już zostało zrobione, należy inaczej zdefiniować inflację. Pierwszy rodzaj to prosta stopa zwrotu czyli =inf-100*(inf-100)/100. Ale tak nie robimy, przechodzimy na logarytmy, bo przekształcają one na całą oś rzeczywistą. I teraz inflacja to przyrost rzeczywistego poziomu cen. |
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traktując szereg czasowy jako jego realizację. |
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Ho: fi_1+fi_2=1 |
H0:delta=0 |
<---- pierwiastek jednostkowy występuje |
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Zastosować test Dickeya i Fullera |
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H1: fi_1+fi_2<1 |
H1:delta<0 |
<------ jest kow. Stacjonarny |
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delta = fi_1+fi_2 - 1 |
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GUS=100*CPI(t)/CPI(t-12) |
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to podaje GUS, ale to naprawdę nie jest inflacja |
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Regresja Dickeya i Fullera: |
prz x(t)=delta * x(t-1) + gamma1*prz x(t-1) + epsilon(t) |
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x(t) ---> |
inflacja=100*[ln(CPI(t))-ln(CPI(t-12))] |
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tak jest w artykułach naukowych |
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GUS |
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r/r |
inflacja |
przy x(t) |
x(t-1) |
przy x(t-1) |
reszty e |
przyrosty reszty |
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rok |
miesiąc |
inflacja GUS |
100*ln( GUS/100 ) |
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gamma1^ |
delta^ |
stała^ |
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2002 |
1 |
103,4 |
3,34347760862374 |
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Student:
0,353669862742025 |
-0,054834386719127 |
0,135368122853691 |
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2 |
103,5 |
3,44014267173323 |
0,09666506310949 |
3,34347760862374 |
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0,082879445871715 |
0,024064914640536 |
0,071782026362217 |
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3 |
103,3 |
3,24671901375014 |
-0,19342365798309 |
3,44014267173323 |
0,09666506310949 |
-0,174341186807873 |
|
0,139773231181049 |
0,355603171590584 |
#N/A |
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4 |
103 |
2,95588022415444 |
-0,290838789595698 |
3,24671901375014 |
-0,19342365798309 |
-0,179766947911132 |
-0,005425761103258 |
10,4802288628559 |
129 |
#N/A |
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5 |
101,9 |
1,88217542405879 |
-1,07370480009565 |
2,95588022415444 |
-0,290838789595698 |
-0,944128128846274 |
-0,764361180935142 |
2,65052566499635 |
16,3125164182414 |
#N/A |
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Oznacza że w tym modelu jest zbyt mało opóźnień bo DW jest zamałe. Założenie o niezależności epsilon(t) nie jest spełnione |
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6 |
101,6 |
1,58733491562902 |
-0,294840508429772 |
1,88217542405879 |
-1,07370480009565 |
0,052736333067897 |
0,99686446191417 |
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1,88582197680815 |
1,97852449147927 |
nieformalnie |
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7 |
101,3 |
1,29162252665462 |
-0,295712388974394 |
1,58733491562902 |
-0,294840508429772 |
-0,239763773064564 |
-0,292500106132461 |
ADF= |
-2,27860300101638 |
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8 |
101,2 |
1,19285708652738 |
-0,098765440127242 |
1,29162252665462 |
-0,295712388974394 |
-0,058723673839527 |
0,181040099225037 |
POZ.IST= |
0,05 |
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9 |
101,3 |
1,29162252665462 |
0,098765440127242 |
1,19285708652738 |
-0,098765440127242 |
0,063737263710301 |
0,122460937549828 |
ASYPT.W.KRYT= |
-1,941 |
bez stałej |
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10 |
101,1 |
1,09399400383343 |
-0,197628522821196 |
1,29162252665462 |
0,098765440127242 |
-0,297101676206629 |
-0,36083893991693 |
ASYPT.W.KRYT= |
-2,861 |
model ze stałą |
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11 |
100,9 |
0,895974137147202 |
-0,198019866686224 |
1,09399400383343 |
-0,197628522821196 |
-0,203504246725225 |
0,093597429481404 |
KONK= |
brak podstaw do odrzucenia H0 |
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12 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
-0,198019866686224 |
-0,115361443685428 |
0,088142803039797 |
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2003 |
1 |
100,5 |
0,498754151103897 |
-0,298062813813791 |
0,796816964917688 |
-0,099157172229514 |
-0,354669063576525 |
-0,239307619891097 |
UWAGA Patrz na DW |
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2 |
100,5 |
0,498754151103897 |
0 |
0,498754151103897 |
-0,298062813813791 |
-0,002603410404265 |
0,352065653172261 |
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3 |
100,6 |
0,598207167754747 |
0,09945301665085 |
0,498754151103897 |
0 |
-0,00856622820344 |
-0,005962817799175 |
DW= |
2,03133920753457 |
chceby by DW=~2 |
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4 |
100,3 |
0,299550897979837 |
-0,29865626977491 |
0,598207167754747 |
0,09945301665085 |
-0,43639560420197 |
-0,42782937599853 |
ro^= |
-0,015669603767286 |
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5 |
100,4 |
0,399202126953746 |
0,099651228973909 |
0,299550897979837 |
-0,29865626977491 |
0,086334517840443 |
0,522730122042413 |
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6 |
100,8 |
0,796816964917688 |
0,397614837963942 |
0,399202126953746 |
0,099651228973909 |
0,248893082445455 |
0,162558564605011 |
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7 |
100,8 |
0,796816964917688 |
0 |
0,796816964917688 |
0,397614837963942 |
-0,232299538421934 |
-0,481192620867388 |
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8 |
100,7 |
0,697561373642536 |
-0,099255591275152 |
0,796816964917688 |
0 |
-0,190930744530186 |
0,041368793891748 |
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9 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
-0,099255591275152 |
0,136398702116277 |
0,327329446646463 |
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10 |
101,3 |
1,29162252665462 |
0,395648389507421 |
0,895974137147202 |
0,198412763504666 |
0,239237844145434 |
0,102839142029157 |
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11 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
0,395648389507421 |
0,091240683631225 |
-0,147997160514209 |
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12 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0,295712388974394 |
-0,054535355243721 |
-0,145776038874946 |
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2004 |
1 |
101,6 |
1,58733491562902 |
-0,098376791013286 |
1,6857117066423 |
0,098376791013286 |
-0,176102852422663 |
-0,121567497178942 |
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|
2 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
-0,098376791013286 |
-0,013534680062647 |
0,162568172360016 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0 |
0,050049204775969 |
0,063583884838616 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,2 |
2,17614917815127 |
0,490437471508969 |
1,6857117066423 |
0,098376791013286 |
0,412711410099591 |
0,362662205323622 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
103,4 |
3,34347760862374 |
1,16732843047247 |
2,17614917815127 |
0,490437471508969 |
0,977835159979914 |
0,565123749880323 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,4 |
4,3059489460447 |
0,962471337420959 |
3,34347760862374 |
1,16732843047247 |
0,597591872965221 |
-0,380243287014693 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,962471337420959 |
-0,048263540723845 |
-0,645855413689066 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,6 |
4,49733656427312 |
0 |
4,49733656427312 |
0,191387618228418 |
0,043552536848363 |
0,091816077572207 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
104,4 |
4,3059489460447 |
-0,191387618228418 |
4,49733656427312 |
0 |
-0,080147048710688 |
-0,123699585559051 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,5 |
4,40168854167743 |
0,095739595632725 |
4,3059489460447 |
-0,191387618228418 |
0,264173575148633 |
0,344320623859321 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
104,5 |
4,40168854167743 |
0 |
4,40168854167743 |
0,095739595632725 |
0,072135559211396 |
-0,192038015937237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
104,4 |
4,3059489460447 |
-0,095739595632725 |
4,40168854167743 |
0 |
0,010256173225074 |
-0,061879385986322 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2005 |
1 |
103,7 |
3,63319292473902 |
-0,67275602130568 |
4,3059489460447 |
-0,095739595632725 |
-0,538149864812737 |
-0,548406038037811 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,6 |
3,53671438372913 |
-0,096478541009886 |
3,63319292473902 |
-0,67275602130568 |
0,205310771710809 |
0,743460636523546 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
103,4 |
3,34347760862374 |
-0,193236775105393 |
3,53671438372913 |
-0,096478541009886 |
-0,100549781370064 |
-0,305860553080873 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
103 |
2,95588022415444 |
-0,387597384469299 |
3,34347760862374 |
-0,193236775105393 |
-0,271285939416738 |
-0,170736158046674 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,5 |
2,46926125903714 |
-0,486618965117302 |
2,95588022415444 |
-0,387597384469299 |
-0,322821694899863 |
-0,051535755483125 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
101,4 |
1,39029051689914 |
-1,078970742138 |
2,46926125903714 |
-0,486618965117302 |
-0,906835975602386 |
-0,584014280702523 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
101,3 |
1,29162252665462 |
-0,098667990244521 |
1,39029051689914 |
-1,078970742138 |
0,223799049031978 |
1,13063502463436 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
-0,098667990244521 |
0,266065489809229 |
0,042266440777251 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
101,8 |
1,7839918128331 |
0,196656897204085 |
1,58733491562902 |
0,295712388974394 |
0,043744750947078 |
-0,222320738862151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
101,6 |
1,58733491562902 |
-0,196656897204085 |
1,7839918128331 |
0,196656897204085 |
-0,303752540930571 |
-0,347497291877649 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
101 |
0,995033085316809 |
-0,592301830312207 |
1,58733491562902 |
-0,196656897204085 |
-0,571077798708083 |
-0,267325257777512 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
100,7 |
0,697561373642536 |
-0,297471711674273 |
0,995033085316809 |
-0,592301830312207 |
-0,168798498501008 |
0,402279300207075 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2006 |
1 |
100,6 |
0,598207167754747 |
-0,099354205887789 |
0,697561373642536 |
-0,297471711674273 |
-0,091265199181365 |
0,077533299319644 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
100,7 |
0,697561373642536 |
0,099354205887789 |
0,598207167754747 |
-0,099354205887789 |
0,031926994568093 |
0,123192193749457 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
100,4 |
0,399202126953746 |
-0,29835924668879 |
0,697561373642536 |
0,099354205887789 |
-0,430615607779018 |
-0,462542602347111 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
100,7 |
0,697561373642536 |
0,29835924668879 |
0,399202126953746 |
-0,29835924668879 |
0,290401801467817 |
0,721017409246836 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
0,29835924668879 |
-0,004225683050623 |
-0,29462748451844 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
0,198412763504666 |
-0,255567717591501 |
-0,251342034540878 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
101,1 |
1,09399400383343 |
0,297177038915738 |
0,796816964917688 |
-0,099157172229514 |
0,240570789153004 |
0,496138506744505 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,6 |
1,58733491562902 |
0,49334091179559 |
1,09399400383343 |
0,297177038915738 |
0,312858716653096 |
0,072287927500092 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
0,49334091179559 |
-0,222807398797089 |
-0,535666115450185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
101,2 |
1,19285708652738 |
-0,394477829101635 |
1,58733491562902 |
0 |
-0,442805415338952 |
-0,219998016541863 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
101,4 |
1,39029051689914 |
0,197433430371762 |
1,19285708652738 |
-0,394477829101635 |
0,266989813974512 |
0,709795229313464 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
101,4 |
1,39029051689914 |
0 |
1,39029051689914 |
0,197433430371762 |
-0,128958649218377 |
-0,395948463192889 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2007 |
1 |
101,6 |
1,58733491562902 |
0,197044398729873 |
1,39029051689914 |
0 |
0,137912003731764 |
0,266870652950141 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
101,9 |
1,88217542405879 |
0,294840508429772 |
1,58733491562902 |
0,197044398729873 |
0,176824256739576 |
0,038912253007812 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
102,5 |
2,46926125903714 |
0,587085834978353 |
1,88217542405879 |
0,294840508429772 |
0,450649445053591 |
0,273825188314015 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,3 |
2,27394869694893 |
-0,195312562088207 |
2,46926125903714 |
0,587085834978353 |
-0,402914824827879 |
-0,853564269881471 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,3 |
2,27394869694893 |
0 |
2,27394869694893 |
-0,195312562088207 |
0,058398626399791 |
0,46131345122767 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
102,6 |
2,56677467485778 |
0,292825977908847 |
2,27394869694893 |
0 |
0,282148437283109 |
0,223749810883318 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
102,3 |
2,27394869694893 |
-0,292825977908847 |
2,56677467485778 |
0,292825977908847 |
-0,391010309034847 |
-0,673158746317956 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,5 |
1,48886124937506 |
-0,785087447573878 |
2,27394869694893 |
-0,292825977908847 |
-0,692201264785295 |
-0,301190955750448 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
102,3 |
2,27394869694893 |
0,785087447573878 |
1,48886124937506 |
-0,785087447573878 |
1,00902188806348 |
1,70122315284878 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103 |
2,95588022415444 |
0,681931527205509 |
2,27394869694893 |
0,785087447573878 |
0,39359221675583 |
-0,615429671307651 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,6 |
3,53671438372913 |
0,580834159574692 |
2,95588022415444 |
0,681931527205509 |
0,366371286401473 |
-0,027220930354358 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,580834159574692 |
0,238498835485148 |
-0,127872450916324 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2008 |
1 |
104 |
3,92207131532813 |
0 |
3,92207131532813 |
0,385356931598998 |
-0,056592880714299 |
-0,295091716199448 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
104,2 |
4,11419433311752 |
0,192123017789389 |
3,92207131532813 |
0 |
0,271819270180395 |
0,328412150894694 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
0,192123017789389 |
-0,073732290919386 |
-0,345551561099781 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
-0,096107647955044 |
4,01817896328318 |
-0,096015369834345 |
0,022816351041033 |
0,096548641960419 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
104,4 |
4,3059489460447 |
0,383877630716568 |
3,92207131532813 |
-0,096107647955044 |
0,497564261768294 |
0,474747910727261 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,383877630716568 |
0,156367616109697 |
-0,341196645658597 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104,8 |
4,68835858988505 |
0,191022025611926 |
4,49733656427312 |
0,191387618228418 |
0,234574562460289 |
0,078206946350592 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,8 |
4,68835858988505 |
0 |
4,68835858988505 |
0,191022025611926 |
0,054156411563133 |
-0,180418150897157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
104,5 |
4,40168854167743 |
-0,28667004820762 |
4,68835858988505 |
0 |
-0,164954903065614 |
-0,219111314628747 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,2 |
4,11419433311752 |
-0,287494208559904 |
4,40168854167743 |
-0,28667004820762 |
-0,080111883100267 |
0,084843019965347 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,7 |
3,63319292473902 |
-0,481001408378501 |
4,11419433311752 |
-0,287494208559904 |
-0,289092170851877 |
-0,20898028775161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,3 |
3,24671901375014 |
-0,38647391098888 |
3,63319292473902 |
-0,481001408378501 |
-0,15250242590229 |
0,136589744949587 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2009 |
1 |
102,8 |
2,76151670329734 |
-0,485202310452802 |
3,24671901375014 |
-0,38647391098888 |
-0,305854412285365 |
-0,153351986383075 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,3 |
3,24671901375014 |
0,485202310452802 |
2,76151670329734 |
-0,485202310452802 |
0,672861696979002 |
0,978716109264367 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
103,6 |
3,53671438372913 |
0,289995369978993 |
3,24671901375014 |
0,485202310452802 |
0,161057658553664 |
-0,511804038425338 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,289995369978993 |
0,341359750281516 |
0,180302091727852 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
0,385356931598998 |
-0,441949812313297 |
-0,783309562594813 |
|
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6 |
103,5 |
3,44014267173323 |
-0,096571711995903 |
3,53671438372913 |
-0,385356931598998 |
0,098282862488214 |
0,540232674801511 |
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7 |
103,6 |
3,53671438372913 |
0,096571711995903 |
3,44014267173323 |
-0,096571711995903 |
0,183996206899356 |
0,085713344411142 |
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8 |
103,7 |
3,63319292473902 |
0,096478541009886 |
3,53671438372913 |
0,096571711995903 |
0,120889478262344 |
-0,063106728637012 |
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9 |
103,4 |
3,34347760862374 |
-0,289715316115279 |
3,63319292473902 |
0,096478541009886 |
-0,259981085465152 |
-0,380870563727495 |
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10 |
103,1 |
3,05292050348228 |
-0,290557105141463 |
3,34347760862374 |
-0,289715316115279 |
-0,140124107732385 |
0,119856977732767 |
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11 |
103,3 |
3,24671901375014 |
0,193798510267862 |
3,05292050348228 |
-0,290557105141463 |
0,328596702418971 |
0,468720810151356 |
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12 |
103,5 |
3,44014267173323 |
0,19342365798309 |
3,24671901375014 |
0,193798510267862 |
0,167546688571673 |
-0,161050013847298 |
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103,6 |
1 |
103,5 |
3,44014267173323 |
0 |
3,44014267173323 |
0,19342365798309 |
-0,015138127792841 |
-0,182684816364514 |
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2 |
102,9 |
2,85874568519127 |
-0,581396986541963 |
3,44014267173323 |
0 |
-0,528126995764864 |
-0,512988867972023 |
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3 |
102,6 |
2,56677467485778 |
-0,291971010333487 |
2,85874568519127 |
-0,581396986541963 |
-0,064958974324842 |
0,463168021440022 |
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4 |
102,4 |
2,37165266173161 |
-0,195122013126175 |
2,56677467485778 |
-0,291971010333487 |
-0,086481273688558 |
-0,021522299363717 |
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5 |
102,2 |
2,17614917815127 |
-0,195503483580335 |
2,37165266173161 |
-0,195122013126175 |
-0,131814711616907 |
-0,045333437928349 |
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6 |
102,3 |
2,27394869694893 |
0,097799518797663 |
2,17614917815127 |
-0,195503483580335 |
0,150902891740674 |
0,282717603357581 |
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7 |
102 |
1,98026272961797 |
-0,293685967330961 |
2,27394869694893 |
0,097799518797663 |
-0,338952250346105 |
-0,489855142086779 |
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8 |
102 |
1,98026272961797 |
0 |
1,98026272961797 |
-0,293685967330961 |
0,077086245222855 |
0,41603849556896 |
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9 |
102,5 |
2,46926125903714 |
0,488998529419169 |
1,98026272961797 |
0 |
0,462216898886823 |
0,385130653663969 |
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10 |
102,8 |
2,76151670329734 |
0,292255444260197 |
2,46926125903714 |
0,488998529419169 |
0,119343705414378 |
-0,342873193472446 |
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11 |
102,7 |
2,66419309464213 |
-0,097323608655208 |
2,76151670329734 |
0,292255444260197 |
-0,184627599526078 |
-0,303971304940455 |
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12 |
103,1 |
3,05292050348228 |
0,388727408840148 |
2,66419309464213 |
-0,097323608655208 |
0,433869107747137 |
0,618496707273215 |
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2011 |
1 |
103,8 |
3,72957847436969 |
0,676657970887414 |
3,05292050348228 |
0,388727408840148 |
0,571213702215863 |
0,137344594468726 |
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2 |
103,6 |
3,53671438372913 |
-0,192864090640558 |
3,72957847436969 |
0,676657970887414 |
-0,363036596818379 |
-0,934250299034242 |
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3 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
-0,192864090640558 |
0,800178875977921 |
1,1632154727963 |
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4 |
104,5 |
4,40168854167743 |
0,191570939813893 |
4,21011760186353 |
0,673403218134398 |
0,048899609946159 |
-0,751279266031762 |
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5 |
105 |
4,87901641694321 |
0,47732787526578 |
4,40168854167743 |
0,191570939813893 |
0,515570776134238 |
0,466671166188079 |
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6 |
104,2 |
4,11419433311752 |
-0,764822083825684 |
4,87901641694321 |
0,47732787526578 |
-0,801468817791933 |
-1,31703959392617 |
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7 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
-0,764822083825684 |
0,26471035182047 |
1,0661791696124 |
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8 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
-0,096015369834345 |
0,310862637576433 |
0,046152285755963 |
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9 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
0,191938638580356 |
-0,356638208256193 |
-0,667500845832626 |
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10 |
104,3 |
4,21011760186353 |
0,384246390154484 |
3,82587121170905 |
-0,384246390154484 |
0,594563936926277 |
0,95120214518247 |
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11 |
104,8 |
4,68835858988505 |
0,478240988021513 |
4,21011760186353 |
0,384246390154484 |
0,437835713816355 |
-0,156728223109922 |
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12 |
104,6 |
4,49733656427312 |
-0,191022025611926 |
4,68835858988505 |
0,478240988021513 |
-0,238446305061099 |
-0,676282018877454 |
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2012 |
1 |
104,1 |
4,01817896328318 |
-0,479157600989943 |
4,49733656427312 |
-0,191022025611926 |
-0,300358297893339 |
-0,06191199283224 |
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2 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
-0,479157600989943 |
0,446368497879907 |
0,746726795773245 |
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3 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
0,191938638580356 |
-0,356638208256193 |
-0,803006706136099 |
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4 |
104 |
3,92207131532813 |
0,096200103619085 |
3,82587121170905 |
-0,384246390154484 |
0,306517650390877 |
0,66315585864707 |
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5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
0,096200103619085 |
-0,339683756650722 |
-0,646201407041599 |
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6 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
-0,385356931598998 |
0,868257792618515 |
1,20794154926924 |
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7 |
104 |
3,92207131532813 |
-0,2880462865354 |
4,21011760186353 |
0,673403218134398 |
-0,430717616403133 |
-1,29897540902165 |
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8 |
103,8 |
3,72957847436969 |
-0,19249284095844 |
3,92207131532813 |
-0,2880462865354 |
-0,010923297945108 |
0,419794318458025 |
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9 |
103,8 |
3,72957847436969 |
0 |
3,72957847436969 |
-0,19249284095844 |
0,137219942149822 |
0,14814324009493 |
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10 |
103,4 |
3,34347760862374 |
-0,386100865745951 |
3,72957847436969 |
0 |
-0,316959840236723 |
-0,454179782386545 |
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11 |
102,8 |
2,76151670329734 |
-0,581960905326403 |
3,34347760862374 |
-0,386100865745951 |
-0,397439243809131 |
-0,080479403572408 |
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12 |
102,4 |
2,37165266173161 |
-0,389864041565732 |
2,76151670329734 |
-0,581960905326403 |
-0,167984056071475 |
0,229455187737656 |
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2013 |
1 |
101,7 |
1,6857117066423 |
-0,685940955089304 |
2,37165266173161 |
-0,389864041565732 |
-0,553377796657554 |
-0,385393740586079 |
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2 |
101,3 |
1,29162252665462 |
-0,39408917998768 |
1,6857117066423 |
-0,685940955089304 |
-0,194425691786819 |
0,358952104870734 |
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Zadanie 1. |
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Przyjmujemy: {x(t)}~AR(1) |
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Sprawdzić występowanie pierwiastka jednostkowego równego jeden dla procesu {xt}, |
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x(t)=fi_1*x(t-1) + epsilon(t), {epsilon}~iiN(0,sigma2) |
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Najpierw, co już zostało zrobione, należy inaczej zdefiniować inflację. Pierwszy rodzaj to prosta stopa zwrotu czyli =inf-100*(inf-100)/100. Ale tak nie robimy, przechodzimy na logarytmy, bo przekształcają one na całą oś rzeczywistą. I teraz inflacja to przyrost rzeczywistego poziomu cen. |
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traktując szereg czasowy jako jego realizację. |
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Ho: fi_1=1 |
H0:delta=0 |
<---- pierwiastek jednostkowy występuje |
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Zastosować test Dickeya i Fullera |
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H1: -1<fi_1<1 |
H1:-2<delta<0 |
<------ jest kow. Stacjonarny |
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GUS=100*CPI(t)/CPI(t-12) |
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to podaje GUS, ale to naprawdę nie jest inflacja |
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Reprametryzacja: |
x(t)-x(t-1)=(fi_1-1)*x(t-1) + epsilon(t) |
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x(t) ---> |
inflacja=100*[ln(CPI(t))-ln(CPI(t-12))] |
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tak jest w artykułach naukowych |
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Regresja Dickeya i Fullera: |
prz x(t)=delta * x(t-1) + epsilon(t) |
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GUS |
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r/r |
inflacja |
przy x(t) |
x(t-1) |
reszty e |
przyrosty reszty |
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rok |
miesiąc |
inflacja GUS |
100*ln( GUS/100 ) |
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delta^ |
stała^ |
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2002 |
1 |
103,4 |
3,34347760862374 |
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Student:
-0,039057025289305 |
0,089614759736685 |
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2 |
103,5 |
3,44014267173323 |
0,09666506310949 |
3,34347760862374 |
0,137636592887047 |
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0,025211615671451 |
0,075280291047993 |
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3 |
103,3 |
3,24671901375014 |
-0,19342365798309 |
3,44014267173323 |
-0,148676678391073 |
-0,28631327127812 |
0,017990423914119 |
0,377156102758296 |
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4 |
103 |
2,95588022415444 |
-0,290838789595698 |
3,24671901375014 |
-0,253646362705076 |
-0,104969684314003 |
2,39992113126146 |
131 |
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5 |
101,9 |
1,88217542405879 |
-1,07370480009565 |
2,95588022415444 |
-1,04787167116538 |
-0,794225308460306 |
0,341380923214955 |
18,6343210860653 |
SSE |
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6 |
101,6 |
1,58733491562902 |
-0,294840508429772 |
1,88217542405879 |
-0,310943095030085 |
0,736928576135298 |
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7 |
101,3 |
1,29162252665462 |
-0,295712388974394 |
1,58733491562902 |
-0,323330568768759 |
-0,012387473738675 |
DF= |
-1,54916788349793 |
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Oznacza że w tym modelu jest zbyt mało opóźnień bo DW jest zamałe. Założenie o niezależności epsilon(t) nie jest spełnione |
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8 |
101,2 |
1,19285708652738 |
-0,098765440127242 |
1,29162252665462 |
-0,137933266176141 |
0,185397302592618 |
POZ.IST= |
0,05 |
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9 |
101,3 |
1,29162252665462 |
0,098765440127242 |
1,19285708652738 |
0,055740129785583 |
0,193673395961724 |
ASYPT.W.KRYT= |
-1,941 |
bez stałej |
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10 |
101,1 |
1,09399400383343 |
-0,197628522821196 |
1,29162252665462 |
-0,236796348870096 |
-0,292536478655679 |
ASYPT.W.KRYT= |
-2,861 |
model ze stałą |
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|
|
|
|
|
|
|
|
|
11 |
100,9 |
0,895974137147202 |
-0,198019866686224 |
1,09399400383343 |
-0,244906474948839 |
-0,008110126078743 |
KONK= |
brak podstaw do odrzucenia H0 |
|
|
|
|
|
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|
|
|
|
|
|
|
|
12 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
-0,153777847433077 |
0,091128627515762 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2003 |
1 |
100,5 |
0,498754151103897 |
-0,298062813813791 |
0,796816964917688 |
-0,356556273200739 |
-0,202778425767661 |
UWAGA Patrz na DW |
|
|
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|
|
|
|
|
|
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|
|
2 |
100,5 |
0,498754151103897 |
0 |
0,498754151103897 |
-0,070134906243874 |
0,286421366956865 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
100,6 |
0,598207167754747 |
0,09945301665085 |
0,498754151103897 |
0,029318110406976 |
0,09945301665085 |
DW= |
1,31894087363387 |
chceby by DW=~2 |
|
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|
4 |
100,3 |
0,299550897979837 |
-0,29865626977491 |
0,598207167754747 |
-0,364906837032354 |
-0,39422494743933 |
ro^= |
0,340529563183064 |
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|
5 |
100,4 |
0,399202126953746 |
0,099651228973909 |
0,299550897979837 |
0,021736036235056 |
0,38664287326741 |
|
|
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|
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|
|
6 |
100,8 |
0,796816964917688 |
0,397614837963942 |
0,399202126953746 |
0,323591725795234 |
0,301855689560178 |
|
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|
7 |
100,8 |
0,796816964917688 |
0 |
0,796816964917688 |
-0,058493459386948 |
-0,382085185182182 |
|
|
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|
|
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|
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|
|
8 |
100,7 |
0,697561373642536 |
-0,099255591275152 |
0,796816964917688 |
-0,1577490506621 |
-0,099255591275152 |
|
|
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|
|
9 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
0,13604267597918 |
0,29379172664128 |
|
|
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|
|
|
|
|
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|
|
|
|
|
|
|
|
10 |
101,3 |
1,29162252665462 |
0,395648389507421 |
0,895974137147202 |
0,341027714303857 |
0,204985038324677 |
|
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|
11 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
0,256544562925494 |
-0,084483151378363 |
|
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|
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|
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|
|
12 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0,07075861121892 |
-0,185785951706574 |
|
|
|
|
|
|
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|
|
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|
|
|
|
2004 |
1 |
101,6 |
1,58733491562902 |
-0,098376791013286 |
1,6857117066423 |
-0,122152665993165 |
-0,192911277212085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
-0,027618179794366 |
0,094534486198799 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
101,7 |
1,6857117066423 |
0,098376791013286 |
1,58733491562902 |
0,07075861121892 |
0,098376791013286 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
4 |
102,2 |
2,17614917815127 |
0,490437471508969 |
1,6857117066423 |
0,46666159652909 |
0,395902985310169 |
|
|
|
|
|
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|
|
|
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|
|
|
|
5 |
103,4 |
3,34347760862374 |
1,16732843047247 |
2,17614917815127 |
1,16270758422014 |
0,696045987691051 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,4 |
4,3059489460447 |
0,962471337420959 |
3,34347760862374 |
1,00344286719852 |
-0,159264717021624 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
7 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,269950415371858 |
-0,733492451826659 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,6 |
4,49733656427312 |
0 |
4,49733656427312 |
0,086037828188646 |
-0,183912587183211 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
9 |
104,4 |
4,3059489460447 |
-0,191387618228418 |
4,49733656427312 |
-0,105349790039772 |
-0,191387618228418 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,5 |
4,40168854167743 |
0,095739595632725 |
4,3059489460447 |
0,174302392776164 |
0,279652182815936 |
|
|
|
|
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|
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|
|
|
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|
|
|
|
|
11 |
104,5 |
4,40168854167743 |
0 |
4,40168854167743 |
0,082302100951254 |
-0,092000291824909 |
|
|
|
|
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|
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|
|
|
|
|
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|
|
|
|
12 |
104,4 |
4,3059489460447 |
-0,095739595632725 |
4,40168854167743 |
-0,01343749468147 |
-0,095739595632725 |
|
|
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|
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|
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|
|
|
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|
|
|
2005 |
1 |
103,7 |
3,63319292473902 |
-0,67275602130568 |
4,3059489460447 |
-0,594193224162241 |
-0,580755729480771 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,6 |
3,53671438372913 |
-0,096478541009886 |
3,63319292473902 |
-0,044191592804115 |
0,550001631358126 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
3 |
103,4 |
3,34347760862374 |
-0,193236775105393 |
3,53671438372913 |
-0,14471799171572 |
-0,100526398911605 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
103 |
2,95588022415444 |
-0,387597384469299 |
3,34347760862374 |
-0,346625854691741 |
-0,201907862976022 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,5 |
2,46926125903714 |
-0,486618965117302 |
2,95588022415444 |
-0,46078583618703 |
-0,114159981495289 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
101,4 |
1,39029051689914 |
-1,078970742138 |
2,46926125903714 |
-1,07214350243457 |
-0,611357666247539 |
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
7 |
101,3 |
1,29162252665462 |
-0,098667990244521 |
1,39029051689914 |
-0,133982138103195 |
0,938161364331374 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,6 |
1,58733491562902 |
0,295712388974394 |
1,29162252665462 |
0,256544562925494 |
0,390526701028689 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
101,8 |
1,7839918128331 |
0,196656897204085 |
1,58733491562902 |
0,16903871740972 |
-0,087505845515775 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
101,6 |
1,58733491562902 |
-0,196656897204085 |
1,7839918128331 |
-0,216594243591035 |
-0,385632961000754 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
101 |
0,995033085316809 |
-0,592301830312207 |
1,58733491562902 |
-0,619920010106573 |
-0,403325766515538 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
100,7 |
0,697561373642536 |
-0,297471711674273 |
0,995033085316809 |
-0,348223439034044 |
0,271696571072528 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2006 |
1 |
100,6 |
0,598207167754747 |
-0,099354205887789 |
0,697561373642536 |
-0,161724293413275 |
0,186499145620769 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
100,7 |
0,697561373642536 |
0,099354205887789 |
0,598207167754747 |
0,033103638630345 |
0,19482793204362 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
100,4 |
0,399202126953746 |
-0,29835924668879 |
0,697561373642536 |
-0,360729334214276 |
-0,393832972844621 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
100,7 |
0,697561373642536 |
0,29835924668879 |
0,399202126953746 |
0,224336134520082 |
0,585065468734358 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
100,9 |
0,895974137147202 |
0,198412763504666 |
0,697561373642536 |
0,13604267597918 |
-0,088293458540902 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
100,8 |
0,796816964917688 |
-0,099157172229514 |
0,895974137147202 |
-0,153777847433077 |
-0,289820523412258 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
101,1 |
1,09399400383343 |
0,297177038915738 |
0,796816964917688 |
0,238683579528791 |
0,392461426961868 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,6 |
1,58733491562902 |
0,49334091179559 |
1,09399400383343 |
0,446454303532975 |
0,207770724004185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
101,6 |
1,58733491562902 |
0 |
1,58733491562902 |
-0,027618179794366 |
-0,474072483327341 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
101,2 |
1,19285708652738 |
-0,394477829101635 |
1,58733491562902 |
-0,422096008896001 |
-0,394477829101635 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
101,4 |
1,39029051689914 |
0,197433430371762 |
1,19285708652738 |
0,154408120030104 |
0,576504128926104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
101,4 |
1,39029051689914 |
0 |
1,39029051689914 |
-0,035314147858674 |
-0,189722267888778 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2007 |
1 |
101,6 |
1,58733491562902 |
0,197044398729873 |
1,39029051689914 |
0,161730250871199 |
0,197044398729873 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
101,9 |
1,88217542405879 |
0,294840508429772 |
1,58733491562902 |
0,267222328635407 |
0,105492077764208 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
102,5 |
2,46926125903714 |
0,587085834978353 |
1,88217542405879 |
0,57098324837804 |
0,303760919742634 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,3 |
2,27394869694893 |
-0,195312562088207 |
2,46926125903714 |
-0,188485322384778 |
-0,759468570762818 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,3 |
2,27394869694893 |
0 |
2,27394869694893 |
-0,000801087973368 |
0,187684234411409 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
102,6 |
2,56677467485778 |
0,292825977908847 |
2,27394869694893 |
0,292024889935479 |
0,292825977908847 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
102,3 |
2,27394869694893 |
-0,292825977908847 |
2,56677467485778 |
-0,282190154257664 |
-0,574215044193143 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
101,5 |
1,48886124937506 |
-0,785087447573878 |
2,27394869694893 |
-0,785888535547246 |
-0,503698381289582 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
102,3 |
2,27394869694893 |
0,785087447573878 |
1,48886124937506 |
0,753623179306301 |
1,53951171485355 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103 |
2,95588022415444 |
0,681931527205509 |
2,27394869694893 |
0,681130439232141 |
-0,07249274007416 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,6 |
3,53671438372913 |
0,580834159574692 |
2,95588022415444 |
0,606667288504963 |
-0,074463150727178 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,433875714988671 |
-0,172791573516292 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2008 |
1 |
104 |
3,92207131532813 |
0 |
3,92207131532813 |
0,063569678812544 |
-0,370306036176127 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
104,2 |
4,11419433311752 |
0,192123017789389 |
3,92207131532813 |
0,255692696601932 |
0,192123017789389 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
-0,024941937457344 |
-0,280634634059276 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
-0,096107647955044 |
4,01817896328318 |
-0,028784290305824 |
-0,003842352848481 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
104,4 |
4,3059489460447 |
0,383877630716568 |
3,92207131532813 |
0,447447309529112 |
0,476231599834936 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,6 |
4,49733656427312 |
0,191387618228418 |
4,3059489460447 |
0,269950415371858 |
-0,177496894157254 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104,8 |
4,68835858988505 |
0,191022025611926 |
4,49733656427312 |
0,277059853800572 |
0,007109438428715 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,8 |
4,68835858988505 |
0 |
4,68835858988505 |
0,093498580273786 |
-0,183561273526787 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
104,5 |
4,40168854167743 |
-0,28667004820762 |
4,68835858988505 |
-0,193171467933834 |
-0,28667004820762 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,2 |
4,11419433311752 |
-0,287494208559904 |
4,40168854167743 |
-0,20519210760865 |
-0,012020639674815 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,7 |
3,63319292473902 |
-0,481001408378501 |
4,11419433311752 |
-0,409927976001499 |
-0,20473586839285 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,3 |
3,24671901375014 |
-0,38647391098888 |
3,63319292473902 |
-0,334186962783108 |
0,075741013218391 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2009 |
1 |
102,8 |
2,76151670329734 |
-0,485202310452802 |
3,24671901375014 |
-0,44800988356218 |
-0,113822920779072 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,3 |
3,24671901375014 |
0,485202310452802 |
2,76151670329734 |
0,50344417843364 |
0,95145406199582 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
103,6 |
3,53671438372913 |
0,289995369978993 |
3,24671901375014 |
0,327187796869615 |
-0,176256381564024 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
0,385356931598998 |
3,53671438372913 |
0,433875714988671 |
0,106687918119056 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
-0,321787252786454 |
-0,755662967775125 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
103,5 |
3,44014267173323 |
-0,096571711995903 |
3,53671438372913 |
-0,048052928606231 |
0,273734324180224 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
103,6 |
3,53671438372913 |
0,096571711995903 |
3,44014267173323 |
0,14131869158792 |
0,189371620194151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
103,7 |
3,63319292473902 |
0,096478541009886 |
3,53671438372913 |
0,144997324399559 |
0,003678632811638 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
103,4 |
3,34347760862374 |
-0,289715316115279 |
3,63319292473902 |
-0,237428367909508 |
-0,382425692309066 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103,1 |
3,05292050348228 |
-0,290557105141463 |
3,34347760862374 |
-0,249585575363905 |
-0,012157207454398 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
103,3 |
3,24671901375014 |
0,193798510267862 |
3,05292050348228 |
0,223421743841922 |
0,473007319205827 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,5 |
3,44014267173323 |
0,19342365798309 |
3,24671901375014 |
0,230616084873712 |
0,00719434103179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
103,6 |
1 |
103,5 |
3,44014267173323 |
0 |
3,44014267173323 |
0,044746979592017 |
-0,185869105281695 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
102,9 |
2,85874568519127 |
-0,581396986541963 |
3,44014267173323 |
-0,536650006949946 |
-0,581396986541963 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
102,6 |
2,56677467485778 |
-0,291971010333487 |
2,85874568519127 |
-0,269931667547965 |
0,266718339401981 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
102,4 |
2,37165266173161 |
-0,195122013126175 |
2,56677467485778 |
-0,184486189474992 |
0,085445478072974 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
102,2 |
2,17614917815127 |
-0,195503483580335 |
2,37165266173161 |
-0,192488545330321 |
-0,00800235585533 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
102,3 |
2,27394869694893 |
0,097799518797663 |
2,17614917815127 |
0,093178672545332 |
0,285667217875654 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
102 |
1,98026272961797 |
-0,293685967330961 |
2,27394869694893 |
-0,294487055304329 |
-0,387665727849662 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
102 |
1,98026272961797 |
0 |
1,98026272961797 |
-0,012271588226528 |
0,282215467077802 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
102,5 |
2,46926125903714 |
0,488998529419169 |
1,98026272961797 |
0,476726941192641 |
0,488998529419169 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
102,8 |
2,76151670329734 |
0,292255444260197 |
2,46926125903714 |
0,299082683963627 |
-0,177644257229014 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
102,7 |
2,66419309464213 |
-0,097323608655208 |
2,76151670329734 |
-0,07908174067437 |
-0,378164424637998 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
103,1 |
3,05292050348228 |
0,388727408840148 |
2,66419309464213 |
0,403168106176493 |
0,482249846850863 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2011 |
1 |
103,8 |
3,72957847436969 |
0,676657970887414 |
3,05292050348228 |
0,706281204461474 |
0,303113098284981 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
103,6 |
3,53671438372913 |
-0,192864090640558 |
3,72957847436969 |
-0,136812609585339 |
-0,843093814046812 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
0,721922001524071 |
0,858734611109409 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104,5 |
4,40168854167743 |
0,191570939813893 |
4,21011760186353 |
0,26639084972414 |
-0,455531151799931 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
105 |
4,87901641694321 |
0,47732787526578 |
4,40168854167743 |
0,559629976217034 |
0,293239126492894 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,2 |
4,11419433311752 |
-0,764822083825684 |
4,87901641694321 |
-0,663876975978884 |
-1,22350695219592 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104,1 |
4,01817896328318 |
-0,096015369834345 |
4,11419433311752 |
-0,024941937457344 |
0,63893503852154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
0,259261996229575 |
0,284203933686919 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
-0,309426480244237 |
-0,568688476473813 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
104,3 |
4,21011760186353 |
0,384246390154484 |
3,82587121170905 |
0,444058779087144 |
0,753485259331381 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
104,8 |
4,68835858988505 |
0,478240988021513 |
4,21011760186353 |
0,55306089793176 |
0,109002118844616 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
104,6 |
4,49733656427312 |
-0,191022025611926 |
4,68835858988505 |
-0,097523445338141 |
-0,650584343269901 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2012 |
1 |
104,1 |
4,01817896328318 |
-0,479157600989943 |
4,49733656427312 |
-0,393119772801297 |
-0,295596327463156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
104,3 |
4,21011760186353 |
0,191938638580356 |
4,01817896328318 |
0,259261996229575 |
0,652381769030872 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
103,9 |
3,82587121170905 |
-0,384246390154484 |
4,21011760186353 |
-0,309426480244237 |
-0,568688476473813 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
104 |
3,92207131532813 |
0,096200103619085 |
3,82587121170905 |
0,156012492551744 |
0,465438972795981 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
103,6 |
3,53671438372913 |
-0,385356931598998 |
3,92207131532813 |
-0,321787252786454 |
-0,477799745338198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
104,3 |
4,21011760186353 |
0,673403218134398 |
3,53671438372913 |
0,721922001524071 |
1,04370925431053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
104 |
3,92207131532813 |
-0,2880462865354 |
4,21011760186353 |
-0,213226376625153 |
-0,935148378149223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
103,8 |
3,72957847436969 |
-0,19249284095844 |
3,92207131532813 |
-0,128923162145896 |
0,084303214479257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
103,8 |
3,72957847436969 |
0 |
3,72957847436969 |
0,05605148105522 |
0,184974643201116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
103,4 |
3,34347760862374 |
-0,386100865745951 |
3,72957847436969 |
-0,330049384690731 |
-0,386100865745951 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
102,8 |
2,76151670329734 |
-0,581960905326403 |
3,34347760862374 |
-0,540989375548846 |
-0,210939990858115 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
102,4 |
2,37165266173161 |
-0,389864041565732 |
2,76151670329734 |
-0,371622173584895 |
0,169367201963951 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2013 |
1 |
101,7 |
1,6857117066423 |
-0,685940955089304 |
2,37165266173161 |
-0,68292601683929 |
-0,311303843254395 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
101,3 |
1,29162252665462 |
-0,39408917998768 |
1,6857117066423 |
-0,417865054967559 |
0,265060961871732 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|