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

被引:123
作者
Douc, R
Moulines, T
Rydén, T
机构
[1] Ecole Natl Super Telecommun Bretagne, CNR, URA 820, F-75634 Paris 13, France
[2] Lund Univ, Ctr Math Sci, S-22100 Lund, Sweden
关键词
asymptotic normality; autoregressive process; consistency; geometric ergodicity; hidden Markov model; identifiability; maximum likelihood; switching autoregression;
D O I
10.1214/009053604000000021
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:2254 / 2304
页数:51
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