Relations between hidden regular variation and the tail order of copulas

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Relations between hidden regular variation and the tail order of copulas

TitleRelations between hidden regular variation and the tail order of copulas
Publication TypeJournal Article
Year of Publication2014
AuthorsHua, L, Joe, H, Li, H
JournalJournal of Applied Probability
Volume51
Pagination37-57
Date PublishedMAR
Type of ArticleArticle
ISSN0021-9002
Keywordsintermediate tail dependence, Multivariate regular variation, Tail dependence, tail order function, upper exponent function
AbstractWe study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.
DOI10.1017/S0021900200010068