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Licensed Unlicensed Requires Authentication Published by De Gruyter (A) March 6, 2013

Properties of hierarchical Archimedean copulas

  • Ostap Okhrin , Yarema Okhrin and Wolfgang Schmid


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.

* Correspondence address: Universität Augsburg, Lehrstuhl für Statistik, Universitätsstr. 16, 86159 Augsburg, Deutschland,

Published Online: 2013-03-06
Published in Print: 2013-03

© by Oldenbourg Wissenschaftsverlag, München, Germany

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