Tracking Interval to Select an Optimal Model Among Non-nested Copula Functions

Abstract

One of the important issues in order to survey multivariate distribution or model dependency structure between interested variables is finding the proper copula function. Extensive studies have been done based on Akaike information criterion (AIC), copula information criterion (CIC), and pseudo-likelihood ratio and fitness test of the copula function. The previous methods of selecting copula functions when the sample size is too small are not satisfactory. Therefore, our method in this paper is based on tracking interval for the parametric copula function which is obtained using expected Kullback–Leibler risk between the two proposed non-nested parametric copula model. It can be find that optimal parametric copula between proposed copula functions in a good level of significance. Finally, efficiency and capability of our method using simulation and applied example have been shown.