Pair-copula constructions of multiple dependence

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 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.

Extensive spatio-temporal assessment of flood events by application of pair-copulas

“…Another possibility to construct copula models of higher dimensions is the use of pair-copulas (Joe, 1996;Aas et al, 2009). They are based on conditional bivariate copulas, which can be coupled by the concept of vines (Bedford and Cooke, 2002).…”

How to Explain Ubiquity of Constant Elasticity of Substitution (CES) Production and Utility Functions Without Explicitly Postulating CES

“…Such an approximation, when copulas are applied to one another like a vine, are known as vine copulas; see, e.g., [1,7,8,10,13,14,15,18,19,21,24].…”

Application of Vine Copulas to Credit Portfolio Risk Modeling

“…Aas et al [29] illustrate a first application of the vine copulas applying non-Gaussian pair copulas to financial data. Apart from many applications to financial data like [30], pair-copula constructions are used in areas as diverse as hydrology, medicine or genetic and evolutionary computation, see [31][32][33], respectively.…”

“…Consequently, very complex and asymmetric dependence structures can be modeled. The specific definition of pair-copulas leads to three fundamental estimation and selection tasks (see e.g., [35]): firstly, estimation of copula parameters for a chosen vine tree structure and pair copula families (for details on estimation of vine copulas like SSP or ML (maximum likelihood) estimation, we refer to [29,[36][37][38] or [39]); secondly, selection of the parametric copula family for each pair copula term and estimation of the corresponding parameters for a chosen vine tree structure; and, thirdly, selection and estimation of all three model components.…”