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.
Fischer,M., & Dörflinger,M. (2010). A note on a non-parametric tail dependence estimator. Far East J. Theor. Stat., 32, 1-5.
6.
Fischer,M., & Hinzmann,G. (2014). A new class of copulas with tail dependence. South African Statist. J., 48, 229-236.
7.
Fischer,M., & Köck,C. (2012). Constructing and generalizing given multivariate copulas: A unifying approach. Statistics, 46, 1-12.
8.
Fischer,M.Köck,C.Schlüther,S., & Weigert,F. (2009). An empirical analysis of multivariate copula model. Quantitative Finance, 9, 839-854.
9.
Genest,C.Ghoudi,K., & Rivest,L.-P. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82, 543-552.
10.
Heffernan,J. (2000). A directory of coefficients of tail dependence. Extremes, 3, 279-290.
11.
Hu,L. (2002). Dependence Patterns across Financial Markets: Methods and Evidence. Working Paper, Ohio State University.
