The Construction and Estimation of Hidden Semi-Markov Models

Abstract

. In this article we construct new formulae and algorithms for Hidden semi-Markov models using Regime Switching Models. We shall include the steps and all necessary lemmas. The formulation of the semi-Markov chain generalizes the one used by Ferguson, by allowing the transition prob- abilities to be duration dependent. However Ferguson supposed that the transition matrix does not depend on the sojourn times. We assume that the transition matrix does depend on the sojourn time.