In this paper, we consider the moderate deviations for the Durbin-Watson statistic related to the stable p-order autoregressive process where the driven noise is also given by a q-order autoregressive process. At first, we establish the moderate deviation principle for the least squares estimators of the unknown vector parameter of the autoregressive process as well as for the serial correlation estimator related with the driven noise.

moderate deviations, Durbin-Watson statistic, serial correlation, p-order autoregressive process.