Explain how residual autocorrelations let you check whether an autoregressive model suits a time series
The idea
To check that an AR model is correctly specified, examine the autocorrelations of its residuals rather than a Durbin–Watson statistic, which is invalid when a lagged dependent variable is a regressor. Each residual autocorrelation has a standard error of one over the square root of T, where T is the number of observations, so its t-statistic is the autocorrelation times the square root of T. If none is significant, the model passes this check, though stationarity and ARCH still need testing. A significant autocorrelation means the model is missing information: add lags, or a seasonal lag if the significant lag is four in quarterly data or twelve in monthly data, and test again. Stopping at lag 1 can miss a problem at a later lag.
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