Nonparametric estimation of simpli ed vine copula models: comparison of methods

Thomas Nagler*, Christian Schellhase, and Claudia Czado Nonparametric estimation of simpli ed vine copula models: comparison of methods DOI 10.1515/demo-2017-0007 Received December 27, 2016; accepted May 16, 2017 Abstract: In the last decade, simpli ed vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. Themost important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.