A goodness-of-fit test for regular vine copula models

We introduce a new goodness-of-fit test for regular vine (R-vine) copula models, a very flexible class of multivariate copulas based on a pair-copula construction (PCC). The test arises from White's information matrix test and extends an existing goodness-of-fit test for copulas. The corresponding critical value can be approximated by asymptotic theory or simulation. The simulation based test shows excellent performance with regard to observed size and power in an extensive simulation study, while the asymptotic theory based test is inadequate for n <= 10,000 for a 5-dimensional model (in d = 8 even 20,000 are not enough). The simulation based test is applied to select among different R-vine specifications modeling the dependency among exchange rates.