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

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

autoregressive process

asymptotic normality

consistency

geometric

ergodicity

hidden Markov model

maximum likelihood

identifiability

switching autoregression

Publication and Content Type

art (subject category)

ref (subject category)