Volume 21, 2017
|Page(s)||183 - 200|
|Published online||19 October 2017|
A note on upper-patched generators for Archimedean copulas
1 Elena Di Bernardino, CNAM, Paris, EA4629, Département IMATH, 292 rue Saint-Martin, Paris cedex 03, France.
2 Didier Rullière, Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, 50 avenue Tony Garnier, 69366 Lyon, France.
Received: 25 July 2016
Revised: 20 December 2016
Accepted: 1 March 2017
The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including d-monotonicity. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.
Mathematics Subject Classification: 62H20 / 62E20 / 60E05 / 62H05
Key words: Archimedean copulas / transformations / distortions / tail dependence coefficients / likelihood
© EDP Sciences, SMAI, 2017
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