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

- Modeling business cycles, economic growth or unemployment.
- Regime-switching time series models.
- 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.