Nonparametric estimation of pair-copula constructions with the empirical pair-copula

A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, which comes at the cost of a large model risk, with errors propagating throughout the vine structure. The empirical pair-copula proposed in the paper provides a nonparametric alternative still achieving the parametric convergence rate. It can be used as a basis for inference on dependence measures, for selecting and pruning the vine structure, and for hypothesis tests concerning the form of the pair-copulae.Comment: 23 pages, 7 figure

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

Risk Measurement and Risk Modelling using Applications of Vine Copulas

__abstract__ This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite nancial risk. Copula-based dependence modelling is a popular tool in nancial applications, but is usuall