A bayesian perspective on mixed GARCH models with jumps

Abstract

In this paper, generalized autoregressive conditionally heteroskedastic (GARCH) models with jumps are investigated, where jump arrivals are time inhomogeneous and state-dependent. These models permit the conditional jump intensity to be time-varying and clustering, and allow volatility effects in the jump component. A Bayesian approach is taken and an efficient adaptive sampling scheme is employed for inference. A Bayesian posterior model comparison procedure is used to compare the proposed model with the standard GARCH model. The proposed methods are illustrated using both simulated and international stock market return series. Our results indicate that the mixed GARCH-Jump models provide a better fit for the dynamics of the daily returns in the US and two Asian markets. © 2013 Springer-Verlag Berlin Heidelberg.