Archimedean copula estimation and model selection via l1-norm symmetric distribution

Based on the relationship between Archimedean copulas and l1-norm symmetric distributions, we propose a method to not only estimate the copula parameter but also select the copula model through the observation data in this paper. The strong consistency of the estimator is proved, and a Radial Information Criteria (RIC) is provided to select the appropriate Archimedean copula model fitting the data best. It can be extended to the multivariate cases conveniently because the selection is achieved by using the one-dimensional radial distribution to capture the dependence structure for multivariate data. The Monte Carlo simulation experiments illustrate that the proposed approach works well in parameter estimation and model selection for both bivariate and multivariate cases. An application in modelling the dependence structure of real stock indices is carried out with good performance as well.