MCMC for Markov-switching models—Gibbs sampling vs. marginalized likelihood

Abstract

This article proposes a method to estimate Markov-switching vector autoregressive models that combines (integrated over latent states) marginal likelihood and Hamiltonian Monte Carlo. The method is compared to commonly used implementations of Gibbs sampling. The proposed method is found to be numerically robust, flexible with respect to model specification and easy to implement using the Stan software package. The methodology is illustrated on a real data application exploring time-varying cointegration relationships in a data set consisting of crude oil and natural gas prices.

Keywords:

• Hamiltonian Monte Carlo
• Markov-switching
• Marginalized likelihood

Acknowledgments

The authors would like to express gratitude to an anonymous referee for many useful comments that considerably improved the article.