Pair-copula constructions of multiple dependence

Kjersti Aas, Claudia Czado, Arnoldo Frigessi, Henrik Bakken

Research output: Contribution to journalArticlepeer-review

1446 Scopus citations


Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically.

Original languageEnglish
Pages (from-to)182-198
Number of pages17
JournalInsurance: Mathematics and Economics
Issue number2
StatePublished - Apr 2009


  • Conditional distribution
  • Decomposition
  • Multivariate distribution
  • Pair-copulae
  • Vines


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