Simplified pair copula constructions-Limitations and extensions

Jakob Stöber, Harry Joe, Claudia Czado

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


So-called pair copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model selection, the simplifying assumption, that copulas of conditional distributions do not depend on the values of the variables which they are conditioned on, is popular.We show that the only Archimedean copulas in dimension d ≥ 3 which are of the simplified type are those based on the Gamma Laplace transform or its extension, while the Student-t copulas are the only one arising from a scale mixture of Normals. Further, we illustrate how PCCs can be adapted for situations where conditional copulas depend on values which are conditioned on, and demonstrate a technique to assess the distance of a multivariate distribution from a nearby distribution that satisfies the simplifying assumption.

Original languageEnglish
Pages (from-to)101-118
Number of pages18
JournalJournal of Multivariate Analysis
StatePublished - Aug 2013


  • Archimedean copula
  • Conditional distribution
  • Elliptical copula
  • Pair copula construction


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