Tail dependence functions and vine copulas

Harry Joe, Haijun Li, Aristidis K Nikoloulopoulos

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199 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)252-270
Number of pages19
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - Jan 2010

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