Testing Copula Hypothesis with Copula Entropy

TL;DR

This paper introduces a new method for testing copula hypotheses using copula entropy, which can be applied universally across different copula types, and demonstrates its effectiveness through simulations.

Contribution

The paper proposes a novel copula hypothesis testing approach based on copula entropy, applicable to any copula function, with specific methods for Gaussian and Gumbel copulas.

Findings

Effective testing method demonstrated via simulations

Applicable to all copula types due to unified entropy approach

Specific estimation techniques for Gaussian and Gumbel copulas

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.