Weighted power mean copulas: theory and application

Article type: Research Article

Authors: Fischer, Matthias^* | Klein, Ingo | Pleier, Thomas

Affiliations: Department of Statistics and Econometrics, University of Erlangen-Nürnberg, Germany

Correspondence: [*] Corresponding author: Matthias Fischer, Department of Statistics and Econometrics, University of Erlangen-Nürnberg, Germany. E-mail: [email protected].

Abstract: It is well known that the arithmetic mean of two possibly different copulas forms a copula, again. More generally, we focus on the weighted power mean (WPM) of two arbitrary copulas which is not necessary a copula again, as different counterexamples reveal. However, various conditions regarding the mean function and the underlying copula are given which guarantee that a proper copula (so-called WPM copula) results. In this case, we also derive dependence properties of WPM copulas and give some brief application to financial return series.

Keywords: Copulas, generalized power mean, max id, left tail decreasing, tail dependence

DOI: 10.3233/MAS-180436

Journal: Model Assisted Statistics and Applications, vol. 13, no. 3, pp. 253-270, 2018