ABSTRACT

Copula based finite mixture models allow us to capture the dependence between random variables more flexibly. Although bivariate case of finite mixture models has been commonly studied, limited efforts have been spent on finite mixture of vines. Instead of using classical mixture models, it is possible to incorporate C-vines into the D-vine model (CD-vine) to understand both the dependence among the variables over different time points. The aim of this study is to create a CD-vine mixture model expressing the dependencies between variables in temporal order. To achieve this, cumulative distribution function values generated within the time components are tied together with D-vine probabilistically. With this approach, dependence structure between variables at each time point is explained by C-vine and the dependence among the time points is captured by the D-vine model. The performance of the proposed CD-vine model is validated using simulated data and applied on four stock market indices.

摘要

基于 Copula 的有限混合模型使我们能够更灵活地捕捉随机变量之间的依赖关系。尽管已经普遍研究了有限混合模型的双变量情况，但在藤蔓的有限混合上花费了有限的努力。可以将 C-vines 合并到 D-vine 模型 (CD-vine) 中，而不是使用经典的混合模型，以了解变量在不同时间点之间的依赖性。本研究的目的是创建一个 CD-vine 混合模型，以时间顺序表达变量之间的依赖关系。为了实现这一点，在时间分量内生成的累积分布函数值与 D-vine 概率性地联系在一起。采用这种方法，C-vine 解释了每个时间点变量之间的依赖结构，D-vine 模型捕获了时间点之间的依赖关系。使用模拟数据验证了所提出的 CD-vine 模型的性能，并应用于四个股票市场指数。