Estimation of Copula Models with Discrete Margins

• 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): Michael Stanley Smith *+ and Mohamad Khaled
• Companies: University of Melbourne and University of Sydney
• Keywords: D-Vine ; Copula Model ; Discrete Time Series; ; Data Augmentation

Abstract

Estimation of copula models with discrete margins is known to be difficult beyond the bivariate case. We show how this can be achieved by augmenting the likelihood with uniform latent variables, and computing inference using the resulting augmented posterior. To evaluate this we propose two efficient Markov chain Monte Carlo sampling schemes. One generates the latent variables as a block using a Metropolis-Hasting step with a proposal that is close to its target distribution. Our method applies to all parametric copulas where the conditional copula functions can be evaluated, not just elliptical copulas as in previous Bayesian work. To demonstrate the potential in higher dimensions we estimate 16 dimensional D-vine copulas for a longitudinal model of usage of a bicycle path in the city of Melbourne, Australia. The estimates reveal an interesting serial dependence structure that can be represented in a parsimonious fashion using Bayesian selection of independence pair-copula components.