Spatially homogeneous copulas

Fabrizio Durante (), Juan Fernández Sánchez () and Wolfgang Trutschnig ()
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Fabrizio Durante: Università del Salento
Juan Fernández Sánchez: Universidad de Almería
Wolfgang Trutschnig: University of Salzburg

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 2, No 11, 607-626

Abstract: 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.

Keywords: Copulas; Dependence; Probability measures; Singular measures (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10463-018-0703-8

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