Changing correlations : a flexible definition of non-Gaussian multivariate dependence

Abstract

Dependencies between variables are often very complex, and may for high values, be different from that of the low values. As the normal distribution and the corresponding copula behave symmetrically for low and high values the frequent application of the normal copula for the description of the dependence may be inappropriate. In this contribution a new way of defining high dimensional multivariate distributions with changing correlations is presented. The method can also be used for a flexible definition of tail dependence. Examples of copulas with linear changing correlations illustrate the methodology. Parameter estimation methods and simulation procedures are discussed. A five dimensional example using groundwater quality data and another four dimensional one using air pollution data, are used to illustrate the methodology.