Pair Copula Constructions for Discrete Data

• Activity Number: 502
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Anastasios Nicholas Panagiotelis*+ and Claudia Czado and Harry Joe
• Companies: Technische Universität München and Technische Universität München and University of British Columbia
• Keywords: Copulas ; Discrete Data ; Vine Pair Copula Constructions

Abstract

Copulas provide a framework for constructing multivariate models with a wide range of dependence features. Unfortunately, applications of copula models to discrete data have been limited to date since the number of times a copula must be evaluated to compute the probability mass function (pmf) grows exponentially with the dimension of the model. Our contribution is to extend vine Pair Copula Constructions (PCCs) to the discrete case. This framework has two major advantages. First, a large degree of flexibility can be achieved by selecting different copula families to be used in the PCC. Secondly, the number of evaluations of copula functions required to compute the pmf only grows quadratically with dimension. Consequently, maximum likelihood estimation is computationally feasible even in high dimensions. We demonstrate the high quality of maximum likelihood estimates and bootstrapped confidence intervals under a simulated setting. We also illustrate the inferential potential of our model in two real data applications. We also address important model selection issues and outline interesting new directions for future research in the modeling of multivariate discrete data.