Bayesian analysis in Markov regime-switching models

Abstract

van Norden and Schaller (1996) develop a standard regime-switching model to study stock market crashes. In their seminal paper, they use the maximum likelihood estimation to estimate the model parameters and show that a two-regime speculative bubble model has significant explanatory power for stock market returns in some observed periods. However, it is well known that the maximum likelihood estimation can lead to bias if the model contains multiple local maximum points or the estimation starts with poor initial values. Therefore, a better approach to estimate the parameters in the regime-switching models is to be found. One possible way is the Bayesian Gibbs-sampling approach, where its advantages are well discussed in Albert and Chib (1993). In this thesis, the Bayesian Gibbs-sampling estimation is examined by using two U.S. stock datasets: CRSP monthly value-weighted index from Jan 1926 to Dec 2010 and S&P 500 index from Jan 1871 to Dec 2010. It is found that the Gibbs-sampling estimation explains the U.S. data better than the maximum likelihood estimation. Moreover, the existing standard regime-switching speculative behaviour model is extended by considering the time-varying transition probabilities which are governed by the first-order Markov chain. It is shown that the time-varying first-order transition probabilities of Markov regime-switching speculative rational bubbles can lead stock market returns to have a second-order Markov regime. In addition, a Bayesian Gibbs-sampling algorithm is developed to estimate the parameters in the second-order two-state Markov regime-switching model.