Issue |
ESAIM: PS
Volume 21, 2017
|
|
---|---|---|
Page(s) | 183 - 200 | |
DOI | https://doi.org/10.1051/ps/2017003 | |
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.
elena.dibernardino@cnam.fr
2 Didier Rullière, Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, 50 avenue Tony Garnier, 69366 Lyon, France.
didier.rulliere@univ-lyon1.fr
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.