Properties of Hierarchical Archimedean Copulas

by Ostap Okhrin of Humboldt-Universität zu Berlin,
Yarema Okhrin of the University of Bern, and
Wolfgang Schmid of the European University Viadrina

March 5, 2009

Abstract: 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 value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

JEL Classification: C16, C46.

Keywords: copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula.

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