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Spatially homogeneous copulas

Author

Listed:
  • Fabrizio Durante

    (Università del Salento)

  • Juan Fernández Sánchez

    (Universidad de Almería)

  • Wolfgang Trutschnig

    (University of Salzburg)

Abstract

We consider spatially homogeneous copulas, i.e. copulas whose corresponding measure is invariant under a special transformations of $$[0,1]^2$$[0,1]2, and we study their main properties with a view to possible use in stochastic models. Specifically, we express any spatially homogeneous copula in terms of a probability measure on [0, 1) via the Markov kernel representation. Moreover, we prove some symmetry properties and demonstrate how spatially homogeneous copulas can be used in order to construct copulas with surprisingly singular properties. Finally, a generalization of spatially homogeneous copulas to the so-called (m, n)-spatially homogeneous copulas is studied and a characterization of this new family of copulas in terms of the Markov $$*$$∗-product is established.

Suggested Citation

  • Fabrizio Durante & Juan Fernández Sánchez & Wolfgang Trutschnig, 2020. "Spatially homogeneous copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 607-626, April.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:2:d:10.1007_s10463-018-0703-8
    DOI: 10.1007/s10463-018-0703-8
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    References listed on IDEAS

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    1. Fredricks, Gregory A. & Nelsen, Roger B. & Rodriguez-Lallena, Jose Antonio, 2005. "Copulas with fractal supports," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 42-48, August.
    2. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Trutschnig, Wolfgang, 2013. "On Cesáro convergence of iterates of the star product of copulas," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 357-365.
    4. Piotr Mikusiński & Michael Taylor, 2010. "Some approximations of n-copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 385-414, November.
    5. Juan Fernández Sánchez & Wolfgang Trutschnig, 2016. "Some members of the class of (quasi-)copulas with given diagonal from the Markov kernel perspective," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1508-1526, March.
    Full references (including those not matched with items on IDEAS)

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