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

TL;DR

This paper presents a new goodness-of-fit test for R-vine copula models, which are flexible multivariate dependency models, demonstrating high performance through simulation and application to exchange rate data.

Contribution

It extends existing copula goodness-of-fit tests to R-vine models using information matrix equality, with a simulation-based approach showing superior accuracy.

Findings

Simulation-based test has excellent size and power performance.

Asymptotic test is inaccurate for small sample sizes (n<10000).

Application to exchange rate data demonstrates practical utility.

Abstract

We introduce a new goodness-of-fit test for regular vine (R-vine) copula models. R-vine copulas are a very flexible class of multivariate copulas based on a pair-copula construction (PCC). The test arises from the information matrix equality and specification test proposed by White (1982) and extends the goodness-of-fit test for copulas introduced by Huang and Prokhorov (2011). 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 inaccurate for n<10000 for a 5-dimensional model (in d=8 even 20000 are not enough). The simulation based test is applied to select among different R-vine specifications to model the dependency among exchange rates.