Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

Randal Douc, Éric Moulines, Tobias Rydén

The Annals of Statistics · 2004 · Volume 32 · Issue 5

Abstract

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.

Keywords

62F12, 62M09, asymptotic normality, autoregressive process, consistency, geometric ergodicity, Hidden Markov model, Identifiability, maximum likelihood, switching autoregression

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