Dynamic linear models with Markov-switching

In this paper, Hamilton's (1988, 1989) Markov-switching model is extended to a general state-space model. This paper also complements Shumway and Stoffer's (1991) dynamic linear models with switching, by introducing dependence in the switching process, and by allowing switching in both measurement and transition equations. Building upon ideas in Hamilton (1989), Cosslett and Lee (1985), and Harrison and Stevens (1976), a basic filtering and smoothing algorithm is presented. The algorithm and the maximum likelihood estimation procedure is applied in estimating Lam's (1990) generalized Hamilton model with a general autoregressive component. The estimation results show that the approximation employed in this paper performs an excellent job, with a considerable advantage in computation time. A state-space representation is a very flexible form, and the approach taken in this paper therefore allows a broad class of models to be estimated that could not be handled before. In addition, the algorithm for calculating smoothed inferences on the unobserved states is a vastly more efficient one than that in the literature.