Tail order and intermediate tail dependence of multivariate copulas

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Tail order and intermediate tail dependence of multivariate copulas

TitleTail order and intermediate tail dependence of multivariate copulas
Publication TypeJournal Article
Year of Publication2011
AuthorsHua, L, Joe, H
JournalJournal of Multivariate Analysis
Volume102
Pagination1454-1471
Date PublishedNOV
Type of ArticleArticle
ISSN0047-259X
KeywordsArchimedean copula, Laplace transform, Max-infinitely divisible, Maximal moment, Reflection symmetry, regular variation, Tail asymmetry
AbstractIn order to study copula families that have tail patterns and tail asymmetry different from multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Archimedean copula, we relate the tail heaviness of a positive random variable to the tail behavior of the Archimedean copula constructed from the Laplace transform of the random variable, and extend the results of Charpentier and Segers [7] [A. Charpentier, J. Segers, Tails of multivariate Archimedean copulas, Journal of Multivariate Analysis 100 (7)(2009) 1521-1537] for upper tails of Archimedean copulas. In addition, a new one-parameter Archimedean copula family based on the Laplace transform of the inverse Gamma distribution is proposed; it possesses patterns of upper and lower tails not seen in commonly used copula families. Finally, tail orders are studied for copulas constructed from mixtures of max-infinitely divisible copulas. (C) 2011 Elsevier Inc. All rights reserved.
DOI10.1016/j.jmva.2011.05.011