On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

Di Bernardino Elena () and Didier Rulliere ()
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Di Bernardino Elena: Conservatoire National des Arts et Métiers, Département IMATH, EA4629, 292 rue Saint Martin, 75011, Paris, France

Dependence Modeling, 2013, vol. 1, issue 2013, 1-36

Abstract: We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.

Keywords: Transformations of Archimedean copulas; self-nested diagonal; non-parametric estimation; tail dependence (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Working Paper: On certain transformation of Archimedean copulas: Application to the non-parametric estimation of their generators (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:1:y:2013:i::p:1-36:n:1

DOI: 10.2478/demo-2013-0001

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