Bivariate temporal dependence via mixtures of rotated copulas

Parametric bivariate copula families have been known to flexibly capture enough various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. However, to the best of our knowledge, there is not a single parametric model adaptable enough to capture several of these features simultaneously. To address this, we propose a mixture of 4-way rotations of a parametric copula that is able to capture all these features. We illustrate the construction using the Clayton family but the concept is general and can be applied to other families. In order to include dynamic dependence regimes, the approach is extended to a time-dependent sequence of mixture copulas in which the mixture probabilities are allowed to evolve in time via a moving average type of relationship. The properties of the proposed model and its performance are examined using simulated and real data sets.