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Operations Management and Econometrics

Pair Copula Constructions for Multivariate Discrete Data

Dr Anastasios Panagiotelis, Monash University

21st Oct 2011  11:00 am - Room 498, Merewether Building (H04)

Rich multivariate discrete datasets are increasingly found in diverse fields including econometrics, finance, biometrics and psychometrics. Many common models used for multivariate discrete data are equivalent to popular copula models, for example the multivariate probit can be expressed in terms of a Gaussian copula. Our contribution is to introduce a new class of models for multivariate discrete data based on Pair Copula Constructions (PCCs) which has two major advantages. First, PCCs capture more flexible dependence structures compared to more restrictive existing approaches, including the Gaussian copula. Second, the computational burden of evaluating the likelihood for an m-dimensional discrete PCC only grows quadratically with m. This compares favourably to existing models for which computing the likelihood either requires the evaluation of evaluation of 2^m terms or slow numerical integration methods. We demonstrate the high quality of maximum likelihood estimates both under a simulated setting and for two real data applications, including a longitudinal discrete dataset. We show that the use of asymmetric pair copulas in a PCC can improve both the in-sample fit of our models and the out-of-sample prediction of joint outcomes that lie in the tails of the multivariate data.