Copula model evaluation based on parametric bootstrap

Copulas are used to model multivariate data as they account for the dependence structure and provide a flexible representation of the multivariate distribution. A great number of copulas has been proposed with various dependence aspects. One important issue is the choice of an appropriate copula from a large set of candidate families to model the data at hand. A large number of copulas are compared via likelihood principle, showing that it is hard to recognize the true underlying copula from real data since copulas with similar dependence properties are very close together. A goodness of fit test based on Mahalanobis squared distance between original and simulated log-likelihoods through parametric bootstrap techniques is also proposed. The advantage of this approach is that it is applicable to all families of copulas.