A geometric investigation into the tail dependence of vine copulas
A geometric investigation into the tail dependence of vine copulas
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DOI：
10.1016/j.jmva.2021.104736
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Emma S. Simpson;J. Wadsworth;J. Tawn
中科院分区：
文献类型：
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作者：
Emma S. Simpson;J. Wadsworth;J. Tawn
藤蔓连接函数是一种多元依赖模型，由一组根据特定的底层图形结构组合的二元连接函数组成。他们的灵活性和实用性，在中等和高的维度作出了贡献的普及藤copula，但相对较少的关注已经支付给他们的极值性质。为了解决这个问题，我们提出了一些研究最广泛的葡萄树copula类的尾部依赖特性的结果。我们的研究重点是尾部依赖系数和样本云的渐近形状，我们使用Nolde（2014）的几何方法计算。我们提供了新的见解，提出了三变量葡萄藤copula构造的结果，从渐近依赖和渐近独立的二元copula，专注于二元极值和反向极值copula，与额外的细节提供了逻辑和反向逻辑的例子。我们还提出了新的理论，一类高维藤copula，构造从二元倒极值copula。
Vine copulas are a type of multivariate dependence model, composed of a collection of bivariate copulas that are combined according to a specific underlying graphical structure. Their flexibility and practicality in moderate and high dimensions have contributed to the popularity of vine copulas, but relatively little attention has been paid to their extremal properties. To address this issue, we present results on the tail dependence properties of some of the most widely studied vine copula classes. We focus our study on the coefficient of tail dependence and the asymptotic shape of the sample cloud, which we calculate using the geometric approach of Nolde (2014). We offer new insights by presenting results for trivariate vine copulas constructed from asymptotically dependent and asymptotically independent bivariate copulas, focusing on bivariate extreme value and inverted extreme value copulas, with additional detail provided for logistic and inverted logistic examples. We also present new theory for a class of higher dimensional vine copulas, constructed from bivariate inverted extreme value copulas.