gofCopula: Goodness-of-Fit Tests for Copulae

Abstract

Last decades show an increased interest in modeling various types of data through copulae. Different copula models have been developed, which lead to the challenge of finding the best fitting model for a particular dataset. From the other side, a strand of literature developed a list of different Goodness-of-Fit (GoF) tests with different powers under different conditions. Usual practice is the selection of the best copula via the p-value of the GoF test. Although this method is not purely correct due to the fact that non-rejection does not imply acception, this strategy is favoured by practitioners. Unfortunately, different GoF tests often provide contradicting outputs. The proposed R-package brings under one umbrella 13 most used copulae - plus their rotated variants - together with 16 GoF tests and a hybrid one. The package offers flexible margin modeling, automatized parallelization, parameter estimation as well as a user friendly interface and pleasant visualizations of the results. To illustrate the functionality of the package, two exemplary applications are provided.