Non-Markovian Regime-Switching Models

This paper revisits the non-Markovian regime switching model considered by Chib and Dueker (2004), who employ an autoregressive continuous latent variable in order to specify the dynamics of the latent regime-indicator variable. We show that, in spite of the non-Markovian nature of the regime indicator variable, the Markovian property of this continuous latent variable allows us to easily estimate the model within the Bayesian framework without any approximations. In particular, we show that the conventional Gibbs sampling is enough in generating the regime indicator variable as well as the continuous latent variable conditional on all the parameters of the model and data. For an application to business cycle modeling of postwar US real GDP, a modified version of Hamilton's (1989) Markovian switching model is slightly preferred to a non-Markovian switching model by the Bayesian model selection criterion. For an application to volatility modeling of the weekly stock return, a non-Markovian switching model with endogenous switching or the leverage effect is strongly preferred to Markovian switching models