Parameter estimation of Markov switching bilinear model using the (EM) algorithm

Markov Switching models have known a strong growth since their introduction by James Hamilton in the late 1980's. These models are used as an essential tool for the analysis of the economic cycles. In this paper, we are interested in a class of bilinear models with markov-switching regime (MS - BL). These models first appeared in Bibi and Aknouche (2010). Parameter estimation via maximum likelihood (ML) of the (MS - BL) model has been considered in Bibi and Ghazel (2015). However, construction and numerical maximization in the approach proposed by Bibi and Ghazel (2015) are computationally intractable. Hence, we propose an expectation-maximization (EM) procedure that provides an alternative method for maximizing the likelihood function in such situations. Convergence and consistency of the (EM) algorithm are discussed in this context. Finally, a Monte Carlo study is presented and two real data examples are proposed. (C) 2017 Elsevier B.V. All rights reserved.