Closed-form likelihood function of Markov-switching models

For a class of Markov-switching models, the likelihood function and inferre d state distributions for a given sample are shown to have closed-form repr esentations under a set of sufficient conditions. Based on these results, i t is demonstrated that the closed-form partial derivatives (when exist) of the likelihood function can be readily found. These results may be used to improve the efficiency of numerical optimization techniques used for estima ting the Markov-switching models. (C) 2001 Elsevier Science B.V. All rights reserved.