Bayesian analysis and model selection of garch models with additive jumps

Abstract

This article investigates parameter estimation and model selection of GARCH models with additive jumps. Continuous noise is driven by Student-t innovations. Since the likelihood is not available in closed form, Bayesian simulation methods are applied to estimate the model parameters and perform model selection. Simulations suggest that the parameters of the jump process are difficult to estimate. Informative priors based on sample moments and tests on jumps are necessary to obtain reliable parameter estimates. In an application using S&P 500returns we estimate a 3% jump intensity. In addition, our model allows us to infer the impact of a jump on future volatility. Our estimates show that the impact of jumps on the conditional volatility is large compared to the impact of continuous innovations.