Non-Markovian Regime-Switching Models

Non-Markovian Regime-Switching Models

To date, almost all extensions and applications of Hamilton’s (1989) regime switching model have been based on the assumption that the latent regimeindicator variable follows a Markovian switching process. This paper doubts the universal validity of this assumption and develops an MCMC algorithm for estimation of the non-Markovian regime switching model which employs an autoregressive continuous latent variable in specifying the dynamics of the discrete latent regime-indicator variable within the Probit specification. We show that, in spite of the non-Markovian nature of the discrete regime indicator variable, the Markovian property of this continuous latent variable allows us to successfully estimate the model. Our empirical results suggest that, for modeling volatility of the stock return, the non-Markovian switching model is strongly preferred to the Markovian switching model. However, for modeling the regime-switching nature of the business cycle based on real GDP, the convention of assuming Markovian switching seems to be valid.