Abstract

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. Paircopula decomposed models also represent a very exible way to construct higher-dimensional coplulae. We apply the methodology to a nancial data set. Our approach represents the rst 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.

Citations