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

2004/10/01 by Randal Douc, Eric Moulines, Éric Moulines +2 · 5 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Financial Risk and Volatility Modeling #Statistical Methods and Inference #math.ST #msc:62F12. #msc:62M09 #stat.TH

paper · pdf · doi:10.1214/009053604000000021

published as Annals of Statistics 2004, Vol. 32, No. 5, 2254-2304 · Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2004/10/01 · arxiv created 2005/03/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Statistical Inference for Probabilistic Functions of Finite State Markov Chains

Cited by

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• Efficient likelihood estimation in state space models
• Estimating the Conditional Forecast-Revision Scale in Sequential Models: Local-Smoothing Limits, Matched Models, and Cost--Accuracy Trade-offs
• Ergodicity and stability of the conditional distributions of nondegenerate Markov chains
• Adaptive estimation of the transition density of a particular hidden Markov chain