Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noise

TL;DR

This paper studies the large sample behavior of the maximum likelihood estimator for autoregressive process coefficients in the presence of stationary Gaussian noise, including simulations for various noise types.

Contribution

It establishes the asymptotic properties of the MLE under mild conditions for AR processes with stationary Gaussian noise, supported by simulation results.

Findings

Asymptotic normality of the MLE established

Valid for fractional Gaussian, AR(1), and MA(1) noise

Simulation confirms theoretical results

Abstract

In this paper we are interested in the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order $p$ with regular stationary Gaussian noise. We exhibit the large sample asymptotical properties of the MLE under very mild conditions. Simulations are done for fractional Gaussian noise (fGn), autoregressive noise (AR(1)) and moving average noise (MA(1)).