A diagnostic for autocorrelation of the disturbances in regression models.

Consider a standard regression model whose disturbances are Gaussian white noise and embed it in a larger model with error terms generated by a first order autoregressive process. We derive a Bayesian diagnostic of the adequacy of the standard model where the autoregressive parameter, say r, is zero against the alternative that r differs from zero. It is shown that it is closely related to the Bayes factor and the Durbin-Watson statistics for the same hypotheses. This formal result is taken as a starting point for some applications where the Bayes factor and the Durbin-Watson statistic play an auxiliary role.