A Bayesian MCMC Algorithm for Markov Switching GARCH models

Markov switching GARCH models have been developed in order to address the statistical regularity observed in financial time series such as strong persistence of conditional variance. However, Maximum Likelihood Estimation faces a implementation problem since the conditional variance depends on all the past history of state. This paper shows that this problem can be handled easily in Bayesian inference. A new Markov Chain Monte Carlo algorithm is introduced and proves to work well in a numerical example.