Consistency of the maximum likelihood estimate for Non-homogeneous Markov-switching models

TL;DR

This paper investigates the theoretical properties of maximum likelihood estimates for a broad class of non-homogeneous Markov-switching models, including their stability and ability to model complex nonlinear time series.

Contribution

It extends existing models by allowing non-homogeneous switching and proves key theoretical results on MLE stability and asymptotic behavior.

Findings

Proves stability of the models under certain conditions

Establishes asymptotic properties of the MLE

Demonstrates the models' ability to capture complex nonlinearities

Abstract

Many nonlinear time series models have been proposed in the last decades. Among them, the models with regime switchings provide a class of versatile and interpretable models which have received a particular attention in the literature. In this paper, we consider a large family of such models which generalize the well known Markov-switching AutoRegressive (MS-AR) by allowing non-homogeneous switching and encompass Threshold AutoRegressive (TAR) models. We prove various theoretical results related to the stability of these models and the asymptotic properties of the Maximum Likelihood Estimates (MLE). The ability of the model to catch complex nonlinearities is then illustrated on various time series.