CHOICE OF PARAMETRIC FAMILIES OF COPULAS

Mariana Craiu (Romania) and Radu V. Craiu (Canada)

Received March 1, 2008

Abstract

Copulas have evolved into a popular tool for modeling dependence in a large number of statistical models. Choosing a copula from an ever increasing set of possibilities presents difficulties that are well recognized in the literature. In this paper we investigate via simulation the effect of copula misspecification on various quantities of interest in the model such as conditional means and conditional variances. We also investigate methods to select among a number of candidate families of parametric copulas using nonparametric kernel smoothing and various distances between distributions. Both the Kullback-Leibler divergence and the Hellinger distance perform very well in this setting.

Keywords and phrases: copulas, Hellinger distance, Kullback-Leibler distance, kernel smoothing, Metropolis-Hastings algorithm.