Efficient goodness-of-fit tests in multi-dimensional vine copula models

TL;DR

This paper presents a new goodness-of-fit test for multivariate vine copula models, demonstrating superior performance in high-dimensional settings through extensive simulations and real data applications.

Contribution

Introduces an information matrix ratio-based goodness-of-fit test for R-vine copulas, with proven asymptotic normality and superior power compared to existing tests.

Findings

The new test outperforms 14 existing tests in size and power.

Simulation results confirm the test's excellent performance.

Application to stock index data validates different R-vine models.

Abstract

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. The corresponding test statistic is derived and its asymptotic normality is proven. 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 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.