The time-varying and asymmetric dependence between crude oil spot and futures markets: Evidence from the Mixture copula-based ARJI–GARCH model

This paper designs a Mixture copula-based ARJI–GARCH model to simultaneously investigate the dynamic process of crude oil spot and futures returns and the time-varying and asymmetric dependence between spot and futures returns. The individual behavior of each market is modeled by the ARJI–GARCH process. The time-varying and asymmetric dependence is captured by the Mixture copula which is composed of the Gumbel copula and Clayton copula. Empirical results show three important findings. First, jumping behavior is an important process for each market. Second, spot and futures returns do not have the same jump process. Third, the tail dependence between spot and futures markets is time-varying and asymmetric with the magnitude of upper tail dependence being slightly weaker than that of lower tail dependence.