Article2008

Multivariate Dependence Modeling using Pair-Copulas

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Financial Risk and Volatility Modeling Statistical Distribution Estimation and Applications Bayesian Modeling and Causal Inference

Abstract

In the copula literature there are many bivariate distribution families but very few higher dimensional ones. Moreover, most of these are difficult to work with. Some of the bivariate families can be extended to more dimensions but in general the construction of distribution functions with more than two variables is a difficult problem. We introduce a construction method that is straightforward to implement and can produce multivariate distribution functions of any dimension. In essence the method takes an arbitrary multivariate density function and decomposes it into a product of bivariate copulas and marginal density functions. Each of these bivariate copulas can be from any of the available families.

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References

1999An Introduction to Copulas 2007Pair-copula constructions of multiple dependence 2007Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask 1998Understanding Relationships Using Copulas 1993Statistical Inference Procedures for Bivariate Archimedean Copulas 2003Modelling Dependence with Copulas and Applications to Risk Management 1986The Joy of Copulas: Bivariate Distributions with Uniform Marginals 1996Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters

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