The Annals of Statistics

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

Randal Douc, Éric Moulines, and Tobias Rydén

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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.

Article information

Ann. Statist., Volume 32, Number 5 (2004), 2254-2304.

First available in Project Euclid: 27 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62F12: Asymptotic properties of estimators

Asymptotic normality autoregressive process consistency geometric ergodicity hidden Markov model identifiability maximum likelihood switching autoregression


Douc, Randal; Moulines, Éric; Rydén, Tobias. Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime. Ann. Statist. 32 (2004), no. 5, 2254--2304. doi:10.1214/009053604000000021.

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