Nonparametric Identification of Copula Structures

Abstract

We propose a unified framework for testing a variety of assumptions commonly made about the structure of copulas, including symmetry, radial symmetry, joint symmetry, associativity and Archimedeanity, and max-stability. Our test is nonparametric and based on the asymptotic distribution of the empirical copula process. We perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on the structure of copulas, particularly when the sample size is moderately large. We illustrate our testing approach on two datasets.

KEY WORDS:

• Archimedeanity
• Associativity
• Asymptotic normality
• Max-stability
• Symmetry
• Test

Acknowledgments

Li's research was partially supported by the National Science Foundation grant DMS-1007686. The authors thank the Editor, an Associate Editor, two anonymous referees, Christian Genest, Ivan Kojadinovic, Johanna Nešlehova, Bruno Rémillard, and Stanislav Volgushev for their helpful comments and suggestions, as well as Jean-François Quessy and Stanislav Volgushev for providing code for their testing procedures.