Nonparametric testing for no covariate effects in conditional copulas

ABSTRACT

In dependence modelling using conditional copulas, one often imposes the working assumption that the covariate influences the conditional copula solely through the marginal distributions. This so-called (pairwise) simplifying assumption is almost standardly made in vine copula constructions. However, in recent literature evidence was provided that such an assumption might not be justified. Among the first issues is thus to test for its appropriateness. In this paper nonparametric tests for the null hypothesis of the simplifying assumption are proposed, and their asymptotic behaviours, under the null hypothesis and under some local alternatives, are established. The tests are fully nonparametric in nature: not requiring choices of copula families nor knowledge of the marginals. In a simulation study, the finite-sample size and power performances of the tests are investigated, and compared with these of the few available tests. A real data application illustrates the use of the tests.

KEYWORDS:

• Conditional copula
• covariate effect
• Kendall's tau
• nonparametric testing
• pairwise simplifying assumption
• partial copula

Acknowledgements

The authors thank the editor, an associate editor and two referees for their very valuable comments that led to a considerable improvement and extension of the original paper version.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Iréne Gijbels http://orcid.org/0000-0002-4443-9803

Marek Omelka http://orcid.org/0000-0002-0396-9373

Additional information

Funding

This research was supported by the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy). The first author gratefully acknowledges support from the GOA/12/014 project of the Research Fund KU Leuven. The second author gratefully acknowledges support from the grant GACR 15-04774Y. The third author is an extraordinary professor at the North-West University, Potchefstroom, South Africa.