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On the structure of exchangeable extreme-value copulas

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  • Mai, Jan-Frederik
  • Scherer, Matthias

Abstract

We show that the set of d-variate symmetric stable tail dependence functions is a simplex and we determine its extremal boundary. The subset of elements which arises as d-margins of the set of (d+k)-variate symmetric stable tail dependence functions is shown to be proper for arbitrary k≥1. Finally, we derive an intuitive and useful necessary condition for a bivariate extreme-value copula to arise as bi-margin of an exchangeable extreme-value copula of arbitrarily large dimension, and thus to be conditionally iid.

Suggested Citation

  • Mai, Jan-Frederik & Scherer, Matthias, 2020. "On the structure of exchangeable extreme-value copulas," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x20302517
    DOI: 10.1016/j.jmva.2020.104670
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    References listed on IDEAS

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    1. Mai, Jan-Frederik & Scherer, Matthias & Shenkman, Natalia, 2013. "Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 457-480.
    2. Clément Dombry & Sebastian Engelke & Marco Oesting, 2016. "Exact simulation of max-stable processes," Biometrika, Biometrika Trust, vol. 103(2), pages 303-317.
    3. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
    4. Gnedin, Alexander V., 1995. "On a class of exchangeable sequences," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 351-355, December.
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    Cited by:

    1. Mai Jan-Frederik, 2022. "About the exact simulation of bivariate (reciprocal) Archimax copulas," Dependence Modeling, De Gruyter, vol. 10(1), pages 29-47, January.

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