Consistency of quasi-maximum likelihood estimator for Markov-switching bilinear time series models

In this paper, we consider the class of Markov switching bilinear processes (MS–BL) that offer remarkably rich dynamics and may be considered as an alternative to model non Gaussian data which exhibit structural changes. In these models, the parameters are allowed to depend upon a latent time-homogeneous Markov chain with finite state space. Analysis based on models with time-varying coefficients has long suffered from the lack of an asymptotic theory except in very restrictive cases. So, first, some basic issues concerning this class of models including sufficient conditions ensuring the existence of stationarity (in strict sense) and ergodic solutions are given. Second, we illustrate the fundamental problems linked with MS–BL models, i.e., parameters estimation by considering a maximum likelihood (ML) approach. So, we provide the detail on the asymptotic properties of ML, in particular, we discuss conditions for its strong consistency.