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Tail-weighted measures of dependence

机译：尾巴加权依赖性

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Multivariate copula models are commonly used in place of Gaussian dependence models when plots of the data suggest tail dependence and tail asymmetry. In these cases, it is useful to have simple statistics to summarize the strength of dependence in different joint tails. Measures of monotone association such as Kendall's tau and Spearman's rho are insufficient to distinguish commonly used parametric bivariate families with different tail properties. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in vine and factor models as well as for assessing the adequacy of fit of multivariate copula models. We apply the tail-weighted measures of dependence to a financial data set and show that the measures better discriminate models with different tail properties compared to commonly used risk measures - the portfolio value-at-risk and conditional tail expectation.
机译：当数据图显示尾部相关性和尾部不对称性时，通常使用多变量copula模型代替高斯相关性模型。在这些情况下，有用简单的统计数据总结不同关节尾部的依附强度是有用的。单调关联的度量（例如Kendall的tau和Spearman的rho）不足以区分具有不同尾部特性的常用参数双变量族。我们提出了较低和较高的尾部加权双变量相关性度量，作为额外的标量度量，以区分具有大致相同的整体单调依赖性的双变量系动词。这些措施可以有效地估计关节尾部的依附强度，并且可以用作在葡萄树和因子模型中选择双变量联接系的指南，以及评估多元系模型的合适性的指南。我们将依赖关系的尾部加权度量应用于财务数据集，结果表明，与常用的风险度量（投资组合风险值和有条件的尾部期望）相比，这些度量更好地区分了具有不同尾部属性的模型。

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