Testing for a \(\delta \)-neighborhood of a generalized Pareto copula (Q2000742)

It is known that a multivariate distribution function \(F\) belongs to the max-domain of attraction of an extreme value distribution if and only if this holds for the copula related to \(F\) and its univariate margins. Furthermore, it is known that a copula fulfills this extreme value condition if and only if the copula is tail equivalent to a generalized Pareto copula. Thus, a \(\chi^2\)-goodness-of-fit test is suggested for testing whether a copula is in a certain neighborhood of a generalized Pareto copula. The test is then transferred to stochastic processes for checking whether the corresponding copula process is in a certain neighborhood of a generalized Pareto process.