B0494
Title: Tree copula mixture distribution for multivariate dependence analysis: An application to energy data
Authors: Federico Bassetti - Univeristy of Pavia (Italy) [presenting]
Maria Elena De Giuli - University of Pavia (Italy)
Enrica Nicolino - Univeristy of Pavia (Italy)
Claudia Tarantola - University of Pavia (Italy)
Abstract: Motivated by the study of the energy market, a Bayesian analysis for a panel AR(p) model is proposed where the multivariate distribution of the innovations is described by a mixture of tree copula distributions. We assume that the innovations of the AR(p) model have normal marginal distributions, without assuming their joint normality. The use of the copulas allows us to split the dependence structure from the marginal distributions. Hence, we can represent a multivariate distribution through its univariate marginal distributions and a copula that captures the dependence structure. Although in the multivariate case the Gaussian and Student$-t$ copulas are the most used, they often are not flexible enough to represent the dependence structure of the data. A possible solution is the use of tree copula: particular types of Markov tree distributions that allow to represent the multivariate joint density through a suitable set of bivariate densities. In particular, in a tree copula the bivariate distributions over the edges of the underlying tree structure are specified by bivariate copulas. In order to develop a more flexible model and to take into account more complex dependence structure, we consider finite mixture of tree copulas. We use a MCMC algorithm to obtain posterior distributions.
