Asymptotic properties of the maximum likelihood estimator for nonlinear AR processes with markov-switching

TL;DR

This paper introduces a new proof approach for the consistency and normality of maximum likelihood estimators in nonlinear AR processes with markov-switching, under specific mixing and forgetting conditions.

Contribution

It provides a novel proof technique applicable to nonlinear AR models with markov-switching, demonstrating the estimator's properties under certain assumptions.

Findings

Assumptions of uniform exponential forgetting and α-mixing are satisfied in linear Gaussian cases.

The new approach confirms the consistency and normality of the MLE in these models.

Applicable to nonlinear AR processes with markov-switching.

Abstract

In this note, we propose a new approach for the proof of the consistency and normality of the maximum likelihood estimator for nonlinear AR processes with markov-switching under the assumptions of uniform exponential forgetting of the prediction filter and $\alpha$-mixing property. We show that in the linear and Gaussian case our assumptions are fully satisfied.