  The purpose of this paper is to investigate moderate deviations for the
Durbin-Watson statistic associated with the stable first-order autoregressive
process where the driven noise is also given by a first-order autoregressive
process. We first establish a moderate deviation principle for both the least
squares estimator of the unknown parameter of the autoregressive process as
well as for the serial correlation estimator associated with the driven noise.
It enables us to provide a moderate deviation principle for the Durbin-Watson
statistic in the easy case where the driven noise is normally distributed and
in the more general case where the driven noise satisfies a less restrictive
Chen-Ledoux type condition.
