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A geometric investigation into the tail dependence of vine copulas

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
Article number104736
<mark>Journal publication date</mark>1/07/2021
<mark>Journal</mark>Journal of Multivariate Analysis
Volume184
Number of pages21
Publication StatusE-pub ahead of print
Early online date15/02/21
<mark>Original language</mark>English

Abstract

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.