gofCopula: Goodness-of-Fit Tests for Copulae

Abstract

Last decades show an increased interest of modeling various types of data through copulae. After copulae have been used for the first time in applications in early 2000s, they gained enormous popularity among academics and practitioners in particular after the pitfall of the Gaussian models in the financial crisis of 2008. Since then different copula models have been developed, which lead to the challenge of finding the best fitting model for a particular dataset. To achieve this, a strand of literature developed a list of different Goodness-of-Fit (GoF) tests with different powers under different conditions. Tests help in solving the issue of identifying the best suited copula model for a given dataset, although different GoF tests often provide contradicting outputs. A hybrid test introduced by Zhang et al. (2016) tackles this issue. The proposed R-package brings under one umbrella several most used copulae with eleven GoF tests together with a hybrid one and offers flexible margin modeling, automatized parallelization, parameter estimation, automative selection of the most suitable copula to the data as well as a user friendly interface and pleasant visualizations of the results. To illustrate the functionality of the package, a simulation study and application is provided.

Keywords: Goodness-of-Fit tests, copula, R-package