Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition

CentER Discussion Paper Series No. 2004-71

35 Pages Posted: 5 Jan 2005

See all articles by John H. J. Einmahl

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research

Laurens de Haan

Erasmus University Rotterdam (EUR) - Department of Econometrics

Deyuan Li

Erasmus University Rotterdam (EUR) - Department of Econometrics

Date Written: August 2004

Abstract

Consider n i.i.d. random vectors on R2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented.

Keywords: Approximations, multivariate analysis

JEL Classification: C12, C14

Suggested Citation

Einmahl, John H. J. and de Haan, Laurens and Li, Deyuan, Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition (August 2004). CentER Discussion Paper Series No. 2004-71, Available at SSRN: https://ssrn.com/abstract=606962 or http://dx.doi.org/10.2139/ssrn.606962

John H. J. Einmahl (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands

Laurens De Haan

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Deyuan Li

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands