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Russell

The second segment is of shorter duration than the first segment. An extract from this segment is presented in Figurę 31 below. Notice that while there is still a "loop" in the data, there is clearly no nearly stationaiy "ellipse" in this extract. this extract again represents one years worth of data.

The third segment is again of relatively short duration. It corresponds well to the "linear" region in the univariate phase map movie extract in Figurę 29. An extract from this segment is provided in Figurę 32. As is the case for the other two segments, one years worth of data is shown. Notice that all of the prior character seen in the data from the first segment is now gone. It is abundantly elear that the underlying model has changed. Notice also that there is no longer any hint of a persistent autocorrelation pattem left in the data.

Models were fit to the first and third segments of the data sets using a standard Box-Jenkins ARIMA modeling procedurę. The first segment (elliptical extract) required an ARIMA(4,1,0) model for a reasonable fit to the data. On the other hand, the third segment (linear extract) required an ARIMA(0,2,1) model with a seasonal (1,0,0) s = 12 component. Notę also that both models reąuired differencing, but of different orders. As expected the third segment did not have an AR component to the fit.

Figurę 31. A representative sample extract from the second segment of the movie. The data in this extract covers the time period from September 1986 to August 1987.