A general autoregressive model with Markov switching: Estimation and consistency

In this paper, a general autoregressive model with Markov switching is considered, where the autoregression may be of an infinite order. The consistency of the maximum likelihood estimators for this model is obtained under regularity assumptions. Examples of finite and infinite order autoregressive models with Markov switching are discussed. Simulation studies with these examples illustrate the consistency and asymptotic normality of the estimators.