Moderate deviations for the mildly stationary autoregressive models with dependent errors

TL;DR

This paper establishes moderate deviation principles for least squares estimators in mildly stationary AR(1) models with dependent errors, providing insights into near-integrated processes and the Durbin-Watson statistic.

Contribution

It introduces new moderate deviation results for estimators in AR(1) models with dependent errors, extending existing theory to mildly stationary and near-integrated cases.

Findings

Moderate deviations for estimators are derived using martingale methods.

Results apply to near-integrated second-order autoregressive processes.

Moderate deviations for the Durbin-Watson statistic are obtained.

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 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.