Copula density estimation by finite mixture of parametric copula densities

Abstract

A copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which are capable of capturing lower tail, strong central, upper tail, heavy tail, and symmetrical elliptical dependence, respectively. The model parameters are estimated by an interior-point algorithm for the constrained maximum likelihood problem. The interior-point algorithm is compared with the commonly used EM algorithm. Simulation and real data application show that the proposed approach is effective to model complex dependencies for data in dimensions beyond two or three.

Keywords:

• Copula
• Dependence modeling
• Mixture model
• Maximum likelihood estimation
• Interior-point algorithm

Acknowledgments

We thank the anonymous referees for insightful and constructive comments which have helped us to significantly improve the paper.

We have used MATLAB functions mvcoprnd() and copulaparam() provided by Robert Kopocinski in MATLAB central file exchange (Kopocinski 2007).

We used multivariate Archimedean copula MATLAB functions provided by Martin Scavnicky in github (Scavnicky 2012).