Asymptotic efficiency in the Autoregressive process driven by a stationary Gaussian noise

TL;DR

This paper investigates the asymptotic properties and efficiency of the maximum likelihood estimator in autoregressive models driven by stationary Gaussian noise, establishing local asymptotic normality and optimal testing procedures.

Contribution

It provides new theoretical results on the asymptotic behavior and efficiency of estimators and tests in Gaussian-driven autoregressive processes.

Findings

Almost sure asymptotic properties of the MLE established

Local asymptotic normality demonstrated for likelihood ratios

Development of an asymptotically optimal testing procedure

Abstract

The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality property of the likelihoods ratio in order to get a notion of asymptotic efficiency and to build an asymptotically uniformly invariant most powerful procedure for testing the significance of the autoregressive parameter.