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

Douc, R (författare)

Moulines, E (författare)

Rydén, Tobias (författare): Lund University,Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH

(creator_code:org_t)

Institute of Mathematical Statistics, 2004
2004
Engelska.
Ingår i: Annals of Statistics. - : Institute of Mathematical Statistics. - 0090-5364 .- 2168-8966. ; 32:5, s. 2254-2304

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Abstract Ämnesord

Stäng

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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