Copula goodness-of-fit testing: an overview and power comparison

Abstract

Several copula goodness-of-fit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different approaches. While no approach is always the best, some stand out and conclusions and recommendations are made. A novel study of p-value variation due to permutation order, for approaches based on Rosenblatt's transformation is also carried out. Results show significant variation due to permutation order for some of the approaches based on this transform. However, when approaching rejection regions, the additional variation is negligible.

Keywords:

• copula
• cramér-von Mises statistic
• empirical copula
• goodness-of-fit
• parametric bootstrap
• pseudo-samples
• Rosenblatt's transformation

Acknowledgements

I would like to thank my colleagues at the Norwegian Computing Center, in particular, Kjersti Aas and Xeni Kristine Dimakos. Credit is also due to my former colleague Henrik Bakken for fruitful discussions and collaboration in the early phase of this work. Finally, I would like to thank the editor, two anonymous referees and colleagues and participants at various workshops and conferences for valuable comments. I mention, in particular, Professors Christian Genest, Nils Lid Hjort, Jean-François Quessy and Mark Salmon. Partial funding in support of this work was provided by the Norwegian Research Council.