Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process

TL;DR

This paper establishes moderate deviation principles for the Durbin-Watson statistic in first-order autoregressive processes, covering both normal and broader noise distributions, advancing statistical inference methods.

Contribution

It introduces new moderate deviation principles for estimators and the Durbin-Watson statistic in autoregressive models with dependent noise.

Findings

Moderate deviation principle for least squares estimator

Moderate deviation principle for serial correlation estimator

Durbin-Watson statistic deviation results under general noise conditions

Abstract

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.