Goodness-of-fit tests for Archimedean copulas in large dimensions

A goodness-of-fit test for exchangeable Archimedean copulas is presented. In a large-scale simulation study it is shown that the test performs well according to the error probability of the first kind and the power under several alternatives, especially in large dimensions. The proposed test is compared to other known tests for Archimedean copulas. In contrast to the latter, the former is simple and easy to apply in any dimension. Commonly applied goodness-of-fit tests are numerically demanding according to precision and runtime, especially as the dimension increases, which is also investigated in this work. The presented goodness-of-fit test is based on a transformation originally intended for sampling random variates from exchangeable Archimedean copulas and its correctness is proven. The proposed goodness-of-fit test may therefore be interpreted as an analogon to the goodness-of-fit test based on Rosenblatt’s transformation which is linked to the conditional distribution method for sampling random variates. Further, it complements in some sense another commonly used goodness-of-fit test based on the probability integral transformation.