Pair-copula constructions of multiple dependence

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 to perform
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
blocs. Pair-copula decomposed models also represent a very flexible
way to construct higher-dimensional coplulae. We apply the
methodology to a financial data set. Our approach represents the
first step towards developing of an unsupervised algorithm that
explores the space of possible pair-copula models, that also can be
applied to huge data sets automatically.