Over the past decades, there has been an increased interest in modelling different types of data through copulae - also in the transport and traffic sector. Different models have been developed for this purpose, which has been a challenge over the years to find the best fitting model for a given data set. As an aid to decision-making, various goodness-of-fit (GoF) tests with different strengths under different conditions were used. The "goodness of fit" allows an assessment of the extent to which and the quality with which a model can explain a set of observations.

However, it turned out that different GoF tests often led to contradictory results. This is where a recent publication in the R Journal (pp. 467-498) by Ostap Okhrin (Head of the Chair of Econometrics and Statistics, esp. in Transport at the TU Dresden), Simon Trimborn (Assistant Professor of Business Statistics at City University of Hong Kong) and Martin Waltz (research assistant to Prof. Ostap Okhrin) comes in.

Under the title "gofCopula: Goodness-of-Fit Tests for Copulae" (PDF download), they propose a package that combines the 13 most commonly used copulae and their rotated variants together with 16 GoF tests and a hybrid test. The package offers "flexible boundary modelling, automated parallelisation, parameter estimation as well as a user-friendly interface and pleasant visualisations of the results," the authors write in the abstract. To illustrate the functionality of the package, two sample applications are provided in the paper.