Moderate deviations for the mildly stationary autoregressive model with dependent errors

Abstract

ABSTRACT 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 modelled 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.