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

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

2005-03-29

arxiv.org/abs/math/0503681v1

Annals of Statistics 2004, Vol. 32, No. 5, 2254-2304

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000021

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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