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FIGURE 21.7 Correlogram of a random walk time series. See Figure 21.6 for definitions.

CHAPTER TWENTY-ONE: TIME SERIES ECONOMETRICS: SOME BASIC CONCEPTS 811

coefficient is about 0.7 at lag 60. Figure 21.7 is the typical correlogram of a nonstationary time series: The autocorrelation coefficient starts at a very high value and declines very slowly toward zero as the lag lengthens.

Now let us take a concrete economic example. Let us examine the correlogram of the GDP time series given in Table 21.1. The correlogram up to 25 lags is shown in Figure 21.8. The GDP correlogram up to 25 lags also shows a pattern similar to the correlogram of the random walk model in Figure 21.7. The autocorrelation coefficient starts at a very high value at lag 1 (0.969) and declines very slowly. Thus it seems that the GDP time series is nonstationary. If you plot the correlograms of the other U.S. economic time series shown in Figures 21.1 and 21.2, you will also see a similar pattern, leading to the conclusion that all these time series are nonstationary; they may be nonstation-ary in mean or variance or both.

Sample: 1970-1 1991-4 Included observations: 88

Autocorrelation

Partial Correlation

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