Summary: J. D. Hamilton’s [J. Econ. Dyn. Control 12, No. 2/3, 385-423 (1988; Zbl 0661.62117); Econometrica 57, No. 2, 357-384 (1989; Zbl 0685.62092)] Markov-switching model is extended to a general state-space model. This paper also complements R. H. Shumway and D. S. Stoffer’s dynamic linear models with switching [forthcoming in J. Am. Stat. Assoc.] by introducing dependence in the switching process, and by allowing switching in both measurement and transition equations. A basic filtering and smoothing algorithm is presented. The algorithm and the maximum likelihood estimation procedure is applied in estimating P. Lam’s [J. Mon. Econ. 26, 409-432 (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.