Controlled Mean-Reverting Estimation for The AR(1) Model with Stationary Gaussian Noise

TL;DR

This paper investigates the maximum likelihood estimator for the mean-reverting parameter in AR(1) models with stationary Gaussian noise, analyzing its asymptotic properties and finite-sample performance.

Contribution

It introduces a Laplace transform-based method to analyze the estimator's asymptotic behavior in models with colored noise, providing new theoretical insights.

Findings

The estimator is asymptotically normal.

Numerical simulations confirm good finite-sample performance.

The method effectively handles stationary Gaussian noise.

Abstract

This paper deals with the maximum likelihood estimator for the mean-reverting parameter of a first order autoregressive models with exogenous variables, which are stationary Gaussian noises (Colored noise). Using the method of the Laplace transform, both the asymptotic properties and the asymptotic design problem of the maximum likelihood estimator are investigated. The numerical simulation results confirm the theoretical analysis and show that the proposed maximum likelihood estimator performs well in finite sample.