Efficient Gibbs sampling for Markov switching GARCH models

Efficient simulation techniques for Bayesian inference on Markov-switching (MS) GARCH models are developed. Different multi-move sampling techniques for Markov switching state space models are discussed with particular attention to MS-GARCH models. The multi-move sampling strategy is based on the Forward Filtering Backward Sampling (FFBS) approach applied to auxiliary MS-GARCH models. A unified framework for MS-GARCH approximation is developed and this not only encompasses the considered specifications, but provides an avenue to generate new variants of MS-GARCH auxiliary models. The use of multi-point samplers, such as the multiple-try Metropolis and the multiple-trial metropolized independent sampler, in combination with FFBS, is considered in order to reduce the correlation between successive iterates and to avoid getting trapped by local modes of the target distribution. Antithetic sampling within the FFBS is also suggested to further improve the sampler's efficiency. The simulation study indicates that the multi-point and multi-move strategies can be more efficient than other MCMC schemes, especially when the MS-GARCH is not strongly persistent. Finally, an empirical application to financial data shows the efficiency and effectiveness of the proposed estimation procedure.