New copulas based on general partitions-of-unity and their applications to risk management (part II)

Abstract

We present a constructive and self-contained approach to data driven in nite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of tting such copulas to highly asymmetric data in arbitrary dimensions.

New copulas based on general partitions-of-unity (part III) — the continuous case

“…The Gamma copula shows an upper tail dependence that coincides precisely with that of the negative binomial copula a particular discrete partition-of-unity copula, see Pfeifer et al ( [6], [7]): , Fig. 7 show the ratios of negative binomial and Gamma copula densities, for various values of a, which also suggest that these copula types are tail-equivalent.…”

“…12 and Fig. 13 show the Power copula densities ( , iven in because t was also used as a data rmer papers on partition-of-unity-copulas (Pfeifer et al [6], [7]). and denote the…”

“…al. [7]. In particular, the following type of a driver is of importance, which is constructed as a patchwork copula with a local Gaussian copula.…”

Multivariate multiple test procedures based on nonparametric copula estimation

“…Usually, the empirical copula or some sort of smoothing method is used. Recently, families of nonparametric copula estimators capable of modeling (positive) tail dependence have been studied by Pfeifer, Mändle, and Ragulina (2017). Further examples comprise kernel (density) estimators (see Gijbels & Mielniczuk, 1990), and beta density estimators (see Chen, 1999).…”

“…Sancetta and Satchell, 2004). Recently, families of nonparametric copula estimators capable of modeling (positive) tail dependence have been studied by Pfeifer, Mändle, and Ragulina (2017). Kernel methods suffer from a boundary bias, although several modifications like the mirror approach by Schuster (1985) exist to address this problem.…”