A New Dynamic Mixture Copula Mechanism to Examine the Nonlinear and Asymmetric Tail Dependence Between Stock and Exchange Rate Returns

This paper develops a new time-varying mixture copula, in which the dynamic weights of four distinct copulas are determined by a two-stratum process, to investigate the magnitude of tail dependence in four independent quadrants. In the two-stratum process, the weight of each copula is determined firstly by the relative importance of positive and negative dependence structures, and then by its own past values and adjustment processes. The weighting mechanism is time-varying in each stratum. This new specification is applied to analyze the asymmetric tail dependencies between the stock and exchange rate markets. Empirical results show four interesting findings. First, the quasi-maximum likelihood estimation (QMLE) has a better fitting ability than does the inference function for margins. The relative efficiency of the QMLE is irrespective of marginal specifications. Second, the goodness-of-fit tests of the new time-varying mixture copula are crucially affected by the marginal specifications. Third, estimation methods impact mixture weights. Four distinct tail dependencies are observed, revealing the importance of considering all four tails concurrently, and not just parts of the four tails. Fourth, the asymmetric positive and negative dependencies are significant. Each country shows a similar pattern of asymmetric negative dependence, but a different pattern of asymmetric positive dependence. These empirical findings provide important portfolio allocation implications.