Beyond simplified pair-copula constructions

Pair-copula constructions (PCCs) offer great flexibility in modeling multivariate dependence. For inference purposes, however, conditional pair-copulas are often assumed to depend on the conditioning variables only indirectly through the conditional margins. The authors show here that this assumption can be misleading. To assess its validity in trivariate PCCs, they propose a visual tool based on a local likelihood estimator of the conditional copula parameter which does not rely on the simplifying assumption. They establish the consistency of the estimator and assess its performance in finite samples via Monte Carlo simulations. They also provide a real data application.