A Comparison of Information Criterion for Choosing Copula Models

Abstract

The object of this paper is to analyse the ability of the Information Criterion in selecting the best copula model. For this study, we carry out a simulation exercise considering five one-parameter copula families: Normal, Student-t with ν degree freedom, Clayton, Gumbel and Frank. For each family copulas, three degrees of dependence and three size samples. The Information Criterion included in the comparison are AIC, BIC, HQIC, SIC. The results obtained are as follow; (i) we find that for a high dependence level (0.9) the reliability of the Information Criterion (IC) is quite good, but it reduces with the dependence level; (ii) the performance of the IC not only depends on the dependence degree but the size sample. In the case of considering negative dependence the reliability of the IC does not depend on the dependence degree but the size sample. As the size sample reduce the performed of the IC reduce. To last, in a comparison among the IC considered, we find that the BIC criterion is the most reliable follow by SIC. AIC and HQIC reaps similar results.