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Reflection invariant copulas
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DOI：10.1016/j.fss.2018.02.004.png)
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Abstract
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In the present paper we study the class of all those copulas that are invariant under a special class of transformations, called reflections. In particular, we focus on the special role played by the independence copula within this class. For this purpose, we introduce a bijective transformation which turns every copula into a reflection invariant copula and enforces a strong geometric property: The n-fold composition of this transformation to a d-dimensional copula coincides with the independence copula on the mesh {0, 1/2(n), . . . , 2(n)-1/2(n), 1}(d). It turns out that the independence copula is the unique fixed point of the introduced transformation. (C) 2018 Elsevier B.V. All rights reserved.
Keywords:
Copula
Reflection invariance
Symmetry
Fixed point
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