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

Elena Di Bernardino () and Didier Rulliere ()
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Elena Di Bernardino: CEDRIC - Centre d'études et de recherche en informatique et communications - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - CNAM - Conservatoire National des Arts et Métiers [CNAM]

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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 $r \in \N$ to $r \in \R$. 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 copula; self-nested diagonal; non-parametric estimation; tail dependence (search for similar items in EconPapers)
Date: 2013-10-21
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-00834000v3
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Citations: View citations in EconPapers (15)

Published in Dependence Modeling, 2013, 1, pp.Pages 1-36, ISSN (Online) 2300-2298. ⟨10.2478/demo-2013-0001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00834000

DOI: 10.2478/demo-2013-0001

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