FULLY BAYESIAN ANALYSIS OF SWITCHING GAUSSIAN STATE SPACE MODELS

SYLVIA FRÜHWIRTH-SCHNATTER

Department of Statistics, University of Business Administration and Economics, Augasse 2-6, A-1090 Vienna, Austria, e-mail: sfruehwi@isis.wu-wien.ac.at

(Received April 12, 2000; revised July 27, 2000)

Abstract. In the present paper we study switching state space models from a Bayesian point of view. We discuss various MCMC methods for Bayesian estimation, among them unconstrained Gibbs sampling, constrained sampling and permutation sampling. We address in detail the problem of unidentifiability, and discuss potential information available from an unidentified model. Furthermore the paper discusses issues in model selection such as selecting the number of states or testing for the presence of Markov switching heterogeneity. The model likelihoods of all possible hypotheses are estimated by using the method of bridge sampling. We conclude the paper with applications to simulated data as well as to modelling the U.S./U.K. real exchange rate.

Key words and phrases: Bayesian analysis, bridge sampling, Markov switching models, MCMC methods, model selection, state space models.