Bayesian Comparison of GARCH Processes with Skewnes Mechanism in Conditional Distributions

Abstract

The main goal of this paper is an application of Bayesian model comparison, based on the posterior probabilities and posterior odds ratios, in testing the explanatory power of the set of competing GARCH (ang. Generalised Autoregressive Conditionally Heteroscedastic) specifications, all with asymmetric and heavy tailed conditional distributions. In building competing volatility models we consider, as an initial specification, GARCH process with conditional Student-t distribution with unknown degrees of freedom parameter, proposed by Bollerslev (1987). By introducing skewness into Student-t family and incorporating the resulting class as a conditional distribution we generated various GARCH models, which compete in explaining possible asymmetry of both conditional and unconditional distribution of financial data. Based on the daily returns of hypothetical financial time series, we discuss the results of Bayesian comparison of alternative skewing mechanisms applied in the initial Student-t GARCH framework. We also check the sensitivity of model ranking with respect to the changes in prior distribution of model specific parameters. Additionally, we present formal Bayesian inference about conditional asymmetry of the distribution of the daily returns in all competing specifications on the basis of the skewness measure defined by Arnold and Groenveld (1995).