The Durbin-Watson test is not an appropriate test statistic in an AR model, so we cannot use it to test for autocorrelation in the residuals. However, we can test whether each of the four lagged residuals autocorrelations is statistically significant. The t-test to accomplish this is equal to the autocorrelation divided by the standard error with 61 degrees of freedom (64 observations less 3 coefficient estimates). The critical t-value for a significance level of 5% is about 2.000 from the table. The appropriate t-statistics are:
- Lag 1 = 0.015/0.129 = 0.116
- Lag 2 = -0.101/0.129 = -0.783
- Lag 3 = -0.007/0.129 = -0.054
- Lag 4 = 0.095/0.129 = 0.736
None of these are statically significant, so we can conclude that there is no evidence of autocorrelation in the residuals, and therefore the AR model is properly specified
