Suppose we decide to use an autoregressive model with a seasonal lag because of the seasonal autocorrelation in the previous problem. We are modeling quarterly data, so we estimate Equation 15: (ln Sales t ˆ’ ln Sales t ˆ’1) = b0 + b1(ln Sales t ˆ’1 - ln Sales t ˆ’2) + b2(ln Sales t ˆ’4 ˆ’ ln Sales t ˆ’5) + ε t. Table 9 shows the regression statistics from this equation.
TABLE 9 Log Differenced Sales: AR(1) Model with Seasonal Lag Johnson & Johnson Quarterly
Observations, January 1985-December 2001
Regression Statistics
R-squared......................0.4220
Standard error.................0.0318
Observations.......................68
Durbin-Watson..............1.8784
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A. Using the information in Table 9, determine if the model is correctly specified.
B. If sales grew by 1 percent last quarter and by 2 percent four quarters ago, use the model to predict the sales growth for this quarter.

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Coefficient Standard Error 0.0053 0.0958 t-Statistic 2.3055 Intercept Lag 1 Lag 4 0.0121 -0.0839 -0.8757 0.6292 0.0958 6.5693 Autocorrelations of the Residual Autocorrelation 0.0572 -0.0700 0.0065 Standard Error t-Statistic Lag 1 0.4720 0.1213 0.1213 -0.5771 0.1213 -0.0532 -0.0368 -0.3033 0.1213