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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Univ Guizhou Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R ChinaUniv Guizhou Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China
Xia, Tian
Wang, Xue-Ren
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Yunnan Univ, Dept Stat, Kunming 650091, Yunnan Province, Peoples R ChinaUniv Guizhou Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China
Wang, Xue-Ren
Jiang, Xue-Jun
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South Univ Sci & Technol, Dept Financial Math & Engn, Shenzhen 518055, Peoples R ChinaUniv Guizhou Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China