Multivariate extreme value copulas with factor and tree dependence structures
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Parsimonious extreme value copula models with O(d) parameters for d observed variables of extrema are presented. These models utilize the dependence characteristics, including factor and tree structures, assumed on the underlying variables that give rise to the data of extremes. For factor structures, a class of parametric models is obtained by taking the extreme value limit of factor copulas with non-zero tail dependence. An alternative model suitable for both factor and tree structures imposes constraints on the parametric Hüsler-Reiss copula to get representations in terms of O(d) other parameters. Dependence properties are discussed. As the full density is often intractable, the method of composite (pairwise) likelihood is used for model inference. Procedures to improve the stability of bivariate density evaluation are also developed. The proposed models are applied to two data examples — one for annual extreme river flows and one for bimonthly extremes of daily stock returns.
KeywordsExtreme value limit Gaussian quadrature Hüsler-Reiss distribution Parsimonious dependence Vine graphical model
AMS 2000 Subject Classifications62H12 62H20 62P12
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This research has been supported by UBC’s Four Year Doctoral Fellowship and NSERC Discovery Grant 8698. We would like to thank the associate editor and the anonymous referees for their helpful comments, which improved the presentation of the paper.
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