Ergodicity of Autoregressive Processes with Markov-Switching and Consistency of the Maximum-Likelihood Estimator

An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.