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.

藤蔓copula是一种多变量依赖模型，由一组双变量copulas组成，它们根据特定的基础图形结构进行组合。它们在中等尺寸和较大尺寸上的柔韧性和实用性促成了藤蔓copulas的普及，但对其极致特性的关注相对较少。为了解决这个问题，我们提出了一些研究最广泛的藤蔓copula类的尾巴依赖特性的结果。我们将研究重点放在样本尾部依赖系数和样本云的渐近形状上，这些样本是使用Nolde（2014）的几何方法计算的。通过介绍由渐近依赖和渐近独立的双变量copulas构成的三变量藤蔓copulas的结果，我们提供了新的见解，着重于双变量极值和倒数极值copula，并为逻辑和倒数逻辑示例提供了更多详细信息。我们还为一类由双变量倒数极值copulas构造的高维藤蔓copulas提供了新的理论。