Penalized estimate of the number of states in Gaussian linear AR with Markov regime

TL;DR

This paper introduces a penalized maximum likelihood method for accurately estimating the number of regimes in Gaussian linear AR processes with Markov regimes, ensuring strong consistency without prior bounds.

Contribution

It proposes a novel penalized likelihood approach for regime number estimation in AR-MR models, with proven strong consistency.

Findings

Method achieves consistent estimation of the number of regimes.

No prior bounds on the number of states are required.

The approach is theoretically validated for AR-MR processes.

Abstract

We deal with the estimation of the regime number in a linear Gaussian autoregressive process with a Markov regime (AR-MR). The problem of estimating the number of regimes in this type of series is that of determining the number of states in the hidden Markov chain controlling the process. We propose a method based on penalized maximum likelihood estimation and establish its strong consistency (almost sure) without assuming previous bounds on the number of states.