Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations

A bivariate generalized autoregressive conditional heteroskedastic model with dynamic conditional correlation and leverage effect (DCC-GJR-GARCH) for modelling financial time series data is considered. For robustness it is helpful to assume a multivariate Student-<italic>t</italic> distribution for the innovation terms. This paper proposes a new modified multivariate <italic>t</italic>-distribution which is a robustifying distribution and offers independent marginal Student-<italic>t</italic> distributions with different degrees of freedom, thereby highlighting the relationship among different assets. A Bayesian approach with adaptive Markov chain Monte Carlo methods is used for statistical inference. A simulation experiment illustrates good performance in estimation over reasonable sample sizes. In the empirical studies, the pairwise relationship between the Australian stock market and foreign exchange market, and between the US stock market and crude oil market are investigated, including out-of-sample volatility forecasts.