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Operations Management and Econometrics

Estimation of copula models with discrete margins

Dr Mohamad Khaled, Discipline of Operations Management and Econometrics, The University of Sydney

19th Nov 2010  11:00 am - Room 498, Merewether Building

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. Moreover, the copula parameters can be estimated joint with any marginal parameters. We establish the effectiveness of the estimation method by modeling consumer behavior in online retail using Archimedean and Gaussian copulas and by estimating 16 dimensional D-vine copulas for a longitudinal model of usage of a bicycle path in the city of Melbourne, Australia. Finally, we extend our results and method to the case where some margins are discrete and others continuous.

The paper is a joint work with Professor Michael S. Smith.