Efficient Gibbs Sampling for Markov Switching GARCH Models

TL;DR

This paper introduces advanced Bayesian inference techniques for switching GARCH models, utilizing multi-move and multi-point sampling strategies to significantly improve the efficiency of Gibbs sampling in Markov Switching GARCH models.

Contribution

It develops novel multi-move and multi-point sampling methods, including FFBS with antithetic sampling, for more efficient Bayesian inference in MS-GARCH models.

Findings

Multi-move strategies outperform single-move Gibbs sampling.

Multi-point samplers like MTM improve sampling efficiency.

Antithetic sampling further enhances the convergence of the sampler.

Abstract

We develop efficient simulation techniques for Bayesian inference on switching GARCH models. Our contribution to existing literature is manifold. First, we discuss different multi-move sampling techniques for Markov Switching (MS) state space models with particular attention to MS-GARCH models. Our multi-move sampling strategy is based on the Forward Filtering Backward Sampling (FFBS) applied to an approximation of MS-GARCH. Another important contribution is the use of multi-point samplers, such as the Multiple-Try Metropolis (MTM) and the Multiple trial Metropolize Independent Sampler, in combination with FFBS for the MS-GARCH process. In this sense we ex- tend to the MS state space models the work of So [2006] on efficient MTM sampler for continuous state space models. Finally, we suggest to further improve the sampler efficiency by introducing the antithetic sampling of Craiu and Meng [2005] and Craiu and Lemieux [2007] within the FFBS. Our simulation experiments on MS-GARCH model show that our multi-point and multi-move strategies allow the sampler to gain efficiency when compared with single-move Gibbs sampling.