Copula Density Estimation by Finite Mixture of Parametric Copulas

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Leming Qu*
• Companies: Boise State University
• Keywords: Copula ; dependence modeling ; mixture model ; maximum likelihood estimation ; interior-point algorithm

Abstract

As a stochastic dependence modeling tool beyond the classical normal distribution model, Copula is widely used in Economics, Finance, and Engineering. A Copula density estimation method that is based on finite mixture of parametric Copula densities is proposed here. More specifically, one component of the mixture model is the mixture of Gaussian, Clayton and Gumble Copulas (termed GCG component) which are capable of capturing symmetrical, lower, and upper tail dependence, respectively. The entire copula density is a mixture of k GCG components.

The model parameters are estimated by interior-point algorithm for the resulting constrained maximum likelihood estimation problem, where the gradient of the objective function is not required. The interior-point algorithm is compared with the expectation-maximization algorithm. Mixture components with small weights can be removed by a thresholding rule. The number of components k is selected by the model selection criterion AIC. Numerical simulation is carried out to study the finite sample performance of the proposed approach.