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LOS e: Explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series.

The regression results from fitting an AR(1) model to the first-differences in enrollment growth rates at a large university includes a Durbin-Watson statistic of 1.58. The number of quarterly observations in the time series is 60. At 5% significance, the critical values for the Durbin-Watson statistic are d_l = 1.55 and d_u = 1.62. Which of the following is the most accurate interpretation of the DW statistic for the model?

A)	Since d_l < DW < d_u, the results of the DW test are inconclusive.

B)	The Durbin-Watson statistic cannot be used with AR(1) models.

C)	Since DW > d_l, the null hypothesis of no serial correlation is rejected.

The Durbin-Watson statistic is not useful when testing for serial correlation in an autoregressive model where one of the independent variables is a lagged value of the dependent variable. The existence of serial correlation in an AR model is determined by examining the autocorrelations of the residuals.

A)	estimate an autoregressive model (for example, an AR(1) model), calculate the autocorrelations for the model's residuals, test whether the autocorrelations are different from zero, and add an AR lag for each significant autocorrelation.

B)	test autocorrelations of the residuals for a simple trend model, and specify the number of significant lags.

C)	estimate an autoregressive model (e.g., an AR(1) model), calculate the autocorrelations for the model's residuals, test whether the autocorrelations are different from zero, and revise the model if there are significant autocorrelations.

The procedure is iterative: continually test for autocorrelations in the residuals and stop adding lags when the autocorrelations of the residuals are eliminated. Even if several of the residuals exhibit autocorrelation, the lags should be added one at a time.

An analyst modeled the time series of annual earnings per share in the specialty department store industry as an AR(3) process. Upon examination of the residuals from this model, she found that there is a significant autocorrelation for the residuals of this model. This indicates that she needs to:

A)	switch models to a moving average model.

B)	alter the model to an ARCH model.

C)	revise the model to include at least another lag of the dependent variable.

She should estimate an AR(4) model, and then re-examine the autocorrelations of the residuals.