On the Robustness of Mixture Models in the Presence of Hidden Markov Regimes with Covariate-Dependent Transition Probabilities

Abstract

We consider general hidden Markov models that may include exogenous co- variates and whose discrete-state-space regime sequence has transition prob- abilities that are functions of observable variables. We show that the param- eters of the observation conditional distribution are consistently estimated by quasi-maximum-likelihood even if the Markov dependence of the hidden regime sequence is not taken into account. Some related numerical results are also discussed.