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
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DOI：
10.1214/009053604000000021
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发表时间：
2004-10-01
影响因子：
4.5
通讯作者：
Rydén, T
中科院分区：
文献类型：
--
作者：
Douc, R;Moulines, T;Rydén, T
具有马尔可夫域的自回归过程是一种每个时间点的回归函数由不可观测马尔可夫链给出的自回归过程。本文研究了一类可能非平稳过程中最大似然估计量的渐近性质，该过程的隐状态空间是紧的，但不一定是有限的。在观测条件下，隐马尔可夫链初始分布的一致指数遗忘证明了一致性和渐近正态性。
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.