ABSTRACT
Hidden Markov models are mixture models with sequential dependence or persistence in the mixture distribution. This chapter discusses the basic modelling choice of specifying the transition distribution of states. It focuses on various considerations that may flow into the specific parameterization of time-varying transition probabilities. The chapter deals with a discussion of an attractive feature of Hidden Markov switching models that has so far, to our knowledge, not been exploited in applied time series modelling. It discusses the estimation of Markov switching models, where the emphasis is on Bayesian estimation. The chapter argues that posterior state identification is obtained by post-processing the posterior draws. It illustrates how to obtain explicit economic interpretations of results from posterior inference. The chapter describes the estimation time and sampler efficiency between using the logit and the probit functional form to estimate the data generating process of a univariate series driven, respectively, by two and three hidden Markov mixtures.
