Testing for a $$\delta $$ δ -neighborhood of a generalized Pareto copula

Stefan Aulbach (), Michael Falk and Timo Fuller
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Stefan Aulbach: University of Würzburg
Michael Falk: University of Würzburg
Timo Fuller: University of Würzburg

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 3, No 6, 599-626

Abstract: Abstract A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the copula corresponding to F and its univariate margins. Aulbach et al. (Bernoulli 18(2), 455–475, 2012. https://doi.org/10.3150/10-BEJ343 ) have shown that a copula satisfies the extreme value condition if and only if the copula is tail equivalent to a generalized Pareto copula (GPC). In this paper, we propose a $$\chi ^2$$ χ 2 -goodness-of-fit test in arbitrary dimension for testing whether a copula is in a certain neighborhood of a GPC. The test can be applied to stochastic processes as well to check whether the corresponding copula process is close to a generalized Pareto process. Since the p value of the proposed test is highly sensitive to a proper selection of a certain threshold, we also present graphical tools that make the decision, whether or not to reject the hypothesis, more comfortable.

Keywords: Multivariate max-domain of attraction; Multivariate extreme value distribution; Copula; D-norm; Generalized Pareto copula; $$\chi ^2$$ χ 2 -goodness-of-fit test; Max-stable processes; Functional max-domain of attraction (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10463-018-0657-x

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