Estimating Non-Simplified Vine Copulas Using Penalized Splines

Understand

Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling.

• Typically, so called simplified vine copula models are estimated where bivariate conditional copulas are approximated by bivariate unconditional copulas.
• We present the first non-parametric estimator of a non-simplified vine copula that allows for varying conditional copulas using penalized hierarchical B-splines.
• Throughout the vine copula, we test for the simplifying assumption in each edge, establishing a data-driven non-simplified vine copula estimator.