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Tail dependence functions and vine copulas
Authors:Harry Joe   Haijun Li  Aristidis K. Nikoloulopoulos  
Affiliation:aDepartment of Statistics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada;bDepartment of Mathematics, Washington State University, Pullman, WA 99164, USA
Abstract:Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated.
Keywords:Archimedean copulas   Conditional tail   D-vine   C-vine   Extreme value
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