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

J.H.J. Einmahl, L.F.M. de Haan, D. Li

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages36
Volume2004-71
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-71

Keywords

  • approximations
  • multivariate analysis

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    Einmahl, J. H. J., de Haan, L. F. M., & Li, D. (2004). Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition. (CentER Discussion Paper; Vol. 2004-71). Econometrics.