  In this paper, we consider the normalized least squares estimator of the
parameter in a mildly stationary first-order autoregressive (AR(1)) model with
dependent errors which are modeled as a mildly stationary AR(1) process. By
martingale methods, we establish the moderate deviations for the least squares
estimators of the regressor and error, which can be applied to understand the
near-integrated second order autoregressive processes. As an application, we
also obtain the moderate deviations for the Durbin-Watson statistic.
