Bayesian analysis of a Markov switching temporal cointegration model

This paper introduces a Bayesian approach to a Markov switching cointegration model that allows the cointegration relationships to be switched on and off depending on the regime. Unlike a classical method for nonlinear cointegration model that uses the cointegrating vector based on a linear cointegration model, the proposed Bayesian method allows for estimation of the cointegrating vector within a nonlinear framework conditional on the regime variables through the Gibbs sampling so that it generates more reliable estimation. The Bayes factors are applied to test for Markov switching and model specifications. The purchasing power parity (PPP) relationship between UK and US is investigated using the proposed model for illustration.