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October 2004 Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
Randal Douc, Éric Moulines, Tobias Rydén
Ann. Statist. 32(5): 2254-2304 (October 2004). DOI: 10.1214/009053604000000021

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.

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Randal Douc. Éric Moulines. Tobias Rydén. "Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime." Ann. Statist. 32 (5) 2254 - 2304, October 2004. https://doi.org/10.1214/009053604000000021

Information

Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62028
MathSciNet: MR2102510
Digital Object Identifier: 10.1214/009053604000000021

Subjects:
Primary: 62M09
Secondary: 62F12

Keywords: asymptotic normality , autoregressive process , consistency , geometric ergodicity , Hidden Markov model , Identifiability , maximum likelihood , switching autoregression

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 5 • October 2004
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