Parametric bivariate copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to construct a model that is adaptable enough to capture several of these features simultaneously. We propose a mixture of 4-way rotations of a parametric copula that can achieve this goal. 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 and seasonal types of relationship. The properties of the proposed model and its performance are examined using simulated and real data sets.

翻译：参数化二元Copula族已被证明能够灵活捕捉多种相依模式，例如二元分布下尾或上尾的正相依或负相依。本文旨在构建一个足够灵活的模型，以同时捕捉这些特征中的若干种。我们提出了一种参数化Copula的四向旋转混合模型来实现这一目标。我们以Clayton族为例说明该构造方法，但该概念具有普适性，可推广至其他Copula族。为纳入动态相依机制，该方法被扩展为混合Copula的时间相依序列，其中混合概率通过移动平均和季节性关系类型随时间演化。通过模拟和实际数据集，我们检验了所提出模型的性质与性能。