Bayesian Estimation of Generalized Hyperbolic Skewed Student GARCH Models

Efficient posterior simulators for two GARCH models with generalized hyperbolic disturbances are presented. The first model, GHt-GARCH, is a threshold GARCH with a skewed and heavy-tailed error distribution; in this model, the latent variables that account for skewness and heavy tails are identically and independently distributed. The second model, ODLV-GARCH, is formulated in terms of observation-driven latent variables; it automatically incorporates a risk premium effect. Both models nest the ordinary threshold t-GARCH as a limiting case. The GHt-GARCH and ODLV-GARCH models are compared with each other and with the threshold t-GARCH using five publicly available asset return data sets, by means of Bayes factors, information criteria, and classical forecast evaluation tools. The GHt-GARCH and ODLV-GARCH models both strongly dominate the threshold t-GARCH, and the Bayes factors generally favor GHt-GARCH over ODLV-GARCH. A Markov switching extension of GHt-GARCH is also presented. This extension is found to be an empirical improvement over the single-regime model for one of the five data sets.