Dependence structure of conditional Archimedean copulas

  • Authors:

  • Mhamed Mesfioui;Jean-François Quessy

  • Affiliations:

  • Département de mathématiques et d'informatique, Université du Québec à Trois-Rivières, C. P. 500, Trois-Rivières (Québec), Canada G9A 5H7;Département de mathématiques et d'informatique, Université du Québec à Trois-Rivières, C. P. 500, Trois-Rivières (Québec), Canada G9A 5H7

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2008

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Abstract

In this article, copulas associated to multivariate conditional distributions in an Archimedean model are characterized. It is shown that this popular class of dependence structures is closed under the operation of conditioning, but that the associated conditional copula has a different analytical form in general. It is also demonstrated that the extremal copula for conditional Archimedean distributions is no longer the Frechet upper bound, but rather a member of the Clayton family. Properties of these conditional distributions as well as conditional versions of tail dependence indices are also considered.