Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models

Abstract

A Markov-switching observation-driven model is a stochastic process ((S_t,Y_t))_t Z where (i) (S_t)_t Z is an unobserved Markov process taking values in a finite set and (ii) (Y_t)_t Z is an observed process such that the conditional distribution of Y_t given all past Y's and the current and all past S's depends only on all past Y's and S_t. In this paper, we prove the consistency and asymptotic normality of the maximum likelihood estimator for such model. As a special case hereof, we give conditions under which the maximum likelihood estimator for the widely applied Markov-switching generalised autoregressive conditional heteroscedasticity model introduced by Haas et al. (2004b) is consistent and asymptotic normal.

Tasks

Reproductions