Gluing Copulas

Abstract

We present a new way of constructing n-copulas, by scaling and gluing finitely many n-copulas. Gluing for bivariate copulas produces a copula that coincides with the independence copula on some grid of horizontal and vertical sections. Examples illustrate how gluing can be applied to build complicated copulas from simple ones. Finally, we investigate the analytical as well as statistical properties of the copulas obtained by gluing, in particular, the behavior of Spearman's ρ and Kendall's τ.

Keywords:

• Construction of copulas
• Copulas
• Horizontal section
• Kendall's tau
• Spearman's rho
• Vertical section

Mathematics Subject Classification:

• 60E05
• 62H05

Acknowledgments

We are grateful to Peter Becker-Kern for interesting discussions, and to one of the anonymous referees for useful comments and remarks. The second author gratefully acknowledges financial support from the German Research Council (SFB 475, Reduction of Complexity in Multivariate Data Structures).