Bayesian Estimation of a Markov-Switching Threshold Asymmetric GARCH Model with Student-t Innovations

A Bayesian estimation of a regime-switching threshold asymmetric GARCH model is proposed. The specification is based on a Markov-switching model with Student-t innovations and K separate GJR(1,1) processes whose asymmetries are located at free non-positive threshold parameters. The model aims at determining whether or not: (i) structural breaks are present within the volatility dynamics; (ii) asymmetries (leverage effects) are present, and are different between regimes; (iii) the threshold parameters (locations of bad news) are similar between regimes. A novel MCMC scheme is proposed which allows for a fully automatic Bayesian estimation of the model. The presence of two distinct volatility regimes is shown in an empirical application to the Swiss Market Index log-returns. The posterior results indicate no differences with regards to the asymmetries and their thresholds when comparing highly volatile periods with the milder ones. Comparisons with a single-regime specification indicates a better in-sample fit and a better forecasting performance for the Markov-switching model.