Testing Copula Hypothesis with Copula Entropy

Abstract: Testing copula hypothesis is of fundamental importance in the applications of copula theory. In this paper we proposed a copula hypothesis testing with copula entropy. Since copula entropy is a unified theory in probability and therefore testing copula hypothesis based on it can be applied to any types of copula function. The test statistic is defined as the difference of copula entropy of copula hypothesis and true copula entropy. We propose the estimation method of the proposed statistic and two special cases for Gaussian copula hypothesis and Gumbel copula hypothesis. We test the effectiveness of the proposed method with simulation experiments.