Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review

We introduce a new goodness-of-fit test for regular vine (R-vine) copula models, a flexible class of multivariate copulas based on a pair-copula construction (PCC). The test arises from the information matrix ratio and assumes fixed margins. The corresponding test statistic is derived and its asymptotic normality is shown. The test's power is investigated and compared to 14 other goodness-of-fit tests, adapted from the bivariate copula case, in a high-dimensional setting. The extensive simulation study on the copula level shows the excellent performance with respect to size and power as well as the superiority of the information matrix ratio based test against most other goodness-of-fit tests. The best performing tests are applied to a portfolio of stock indices and their related volatility indices validating different R-vine specifications.