The new family of Fisher copulas to model upper tail dependence and radial asymmetry: Properties and application to high‐dimensional rainfall data

Abstract

Joint precipitation data measured at a large number of stations typically show tail asymmetry and significant upper tail dependence. Unfortunately, many multivariate dependence models that are commonly used in large dimensions such as the normal and the Student copulas are radially symmetric, whereas the recently introduced chi‐square copula is asymmetric, but its tail dependence coefficients are null. In order to circumvent the limitations of the available models, the new family of Fisher copulas is introduced; it is shown that these dependence models are tail asymmetric and allow for upper tail dependence, among other characteristics. Two semiparametric strategies for parameter estimation in this class of copulas are proposed, and their efficiency in small and moderate sample sizes is investigated with the help of simulations. The usefulness of the parametric Fisher copula family is then illustrated on the modeling of the precipitation data observed at 105 stations within or close to the Aare river catchment in Switzerland.