Journal
STATISTICS & RISK MODELING
Volume 30, Issue 1, Pages 21-53Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1524/strm.2013.1071
Keywords
copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula
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In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula values, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures, and extreme value copulas. We pay special attention to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.
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