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95% confidence interval 95% confidence interval

FIGURE 22.2 Correlogram and partial correlogram, GDP, United States, 1970-I to 1991-IV.

95% confidence interval 95% confidence interval

FIGURE 22.2 Correlogram and partial correlogram, GDP, United States, 1970-I to 1991-IV.

7In time series data a large proportion of correlation between Yt and Yt—k may be due to the correlations they have with the intervening lags Yt—i, Yt—2, • • •, Yt-k+l. The partial correlation Pkk removes the influence of these intervening variables.

CHAPTER TWENTY-TWO: TIME SERIES ECONOMETRICS: FORECASTING 843

very slowly; as shown in Figure 21.8, ACF up to 23 lags are individually statistically significantly different from zero, for they all are outside the 95% confidence bounds. Second, after the first lag, the PACF drops dramatically, and all PACFs after lag 1 are statistically insignificant.

Since the U.S. GDP time series is not stationary, we have to make it stationary before we can apply the Box-Jenkins methodology. In Figure 21.9 we plotted the first differences of GDP. Unlike Figure 21.1, we do not observe any trend in this series, perhaps suggesting that the first-differenced GDP time series is stationary.8 A formal application of the Dickey-Fuller unit root test shows that that is indeed the case. We can also see this visually from the estimated ACF and PACF correlograms given in Figure 22.3. Now we have a much different pattern of ACF and PACF. The ACFs at lags 1, 8, and 12 seem statistically different from zero; recall from Chapter 21 that the

Lag

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