Nonparametric identification of copula structures

Li, Bo; Genton, Marc G.

Type

Article

Authors

Li, Bo
Genton, Marc G.

KAUST Department

Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Spatio-Temporal Statistics and Data Analysis Group
Statistics Program

Date

2013-06

Permanent link to this record

http://hdl.handle.net/10754/562798

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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. © 2013 American Statistical Association.

Sponsors

Bo Li is Assistant Professor, Department of Statistics, Purdue University, West Lafayette, IN 47907-2066 (E-mail: boli@purdue.edu). Marc G. Genton is Professor, CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia (E-mail: marc.genton@kaust.edu.sa). 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 Neslehova, Bruno Remillard, and Stanislav Volgushev for their helpful comments and suggestions, as well as Jean-Francois Quessy and Stanislav Volgushev for providing code for their testing procedures.