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

Author

Listed:
  • Stefan Aulbach

    (University of Würzburg)

  • Michael Falk

    (University of Würzburg)

  • Timo Fuller

    (University of Würzburg)

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.

Suggested Citation

  • Stefan Aulbach & Michael Falk & Timo Fuller, 2019. "Testing for a $$\delta $$ δ -neighborhood of a generalized Pareto copula," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 599-626, June.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0657-x
    DOI: 10.1007/s10463-018-0657-x
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    References listed on IDEAS

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    6. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
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