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

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 (2013). 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.

U.S. stock markets and the role of real interest rates

“…If the test shows that the two models are not statistically different, we use the C-vine. Finally, we apply the goodnessof-fit test proposed by Schepsmeier (2013) to verify that the selected vine copula model is appropriate.…”

Multivariate dependence risk and portfolio optimization: An application to mining stock portfolios

“…In order to confirm empirically our judgment about the r-vine being the most adequate model to capture the multivariate dependence structure of the gold portfolio, we run on the fit of the c-vine, d-vine and r-vine to the portfolios the ECP and ECP2 goodness-of-fit tests, which are based on the empirical copula processes. For further details on the goodness of fit tests see Schepsmeier (2013Schepsmeier ( , 2014, and Genest et al (2009). The ECP and ECP2 goodness-of-fit tests implemented are non-parametric and are based on the Cramer-von Mises (CvM) and Kolmogorov-Smirnov (KS) test statistics.…”

Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data

“…These results are then used to derive robust hypothesis testing methods for possibly misspecified models in the presence of ignorable or nonignorable missing-data mechanisms. Second, a method for the detection of model misspecification in missing data problems is discussed using recently developed Generalized Information Matrix Tests (GIMT) (Golden et al 2013(Golden et al , 2016; also see Cho and White 2014;Cho and Phillips 2018;Huang and Prokhorov 2014;Ibragimov and Prokhorov 2017;Prokhorov et al 2019;Schepsmeier 2015Schepsmeier , 2016Zhu 2017). Third, we provide regularity conditions for the Missing Information Principle (MIP) to hold in the presence of model misspecification in order to provide useful computational covariance matrix estimation formulas.…”