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Higher order tail densities of copulas and hidden regular variation

Haijun Li and Lei Hua

Journal of Multivariate Analysis, 2015, vol. 138, issue C, 143-155

Abstract: A notion of higher order tail densities for copulas is introduced using multivariate regular variation of copula densities, and densities of multivariate extremes with various margins can then be studied in a unified fashion. We show that the tail of a multivariate density can be decomposed into the tail density of the underlying copula, coupled with marginal tail transforms of the three types: Fréchet, Gumbel, and Weibull types. We also derive the relation between the tail density and tail order functions of a copula in the context of hidden regular variation. Some illustrative examples are given.

Keywords: Multivariate regular variation; Tail dependence; Upper exponent function; Tail order function (search for similar items in EconPapers)
Date: 2015
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