Finite Mixtures of Archimedean Copulas

• Activity Number: 344
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Renate Meyer*+ and Goeran Kauermann
• Companies: University of Auckland and Ludwig-Maxilians-Universität München
• Keywords: Archimedean copula ; finite mixture model ; penalized marginal likelihood ; Markov chain Monte Carlo ; quadratic programming

Abstract

Copulas allow for stochastic modelling of multivariate distributions with a flexibility well beyond that of the classical normal distribution. To further increase the versatility we propose the use of mixtures of different Archimedean copula families like Clayton, Frank, Gumbel, etc. Using a Bayesian approach, each family-specific parameter is modelled by imposing a prior distribution on the parameter. The mixture model itself is fitted in two ways. We first present a fully Bayesian approach with MCMC-based posterior computation. Then, a computationally much faster marginal likelihood estimate is proposed using a penalized version of a classical quadrature which approximates the integrals. The performance of the new approach is evaluated on simulations and an example in the context of modelling the dependence structure of the log-returns of exchange rates.