Multivariate Archimedean copula model selection via l1-norm symmetric distribution

Copula techniques have been increasing the interest in practical applications such as signal processing, communication and control, because they provide a general method for modelling dependencies. Based on the relationship between Archimedean copula and l₁-norm symmetric distribution, the selection of multivariate model can be reduced to a one-dimensional problem. So, a radial information criteria (RIC) using the distribution of the radial part of the l₁-norm symmetric distribution to capture the dependence structure of multivariate data is proposed in this paper. The new method provides a general framework to justify which copula model fits the data best among the Archimedean copula families. Especially, it differs from the Bayesian approach which requires the prior probability information, and can deal with the case of multivariate data which is difficult to extend from bivariate case using existing methods. The Monte Carlo simulation experiments illustrate that the proposed approach works well in multivariate model selection among lower tail dependence, upper tail dependence and symmetric dependence.