Testing goodness of fit for parametric families of copulas - Application to financial data

This article suggests a chi-square test of fit for parametric families of bivariate copulas. The marginal distribution functions are assumed to be unknown and are estimated by their empirical counterparts. Therefore, the standard asymptotic theory of the test is not applicable, but we derive a rule for the determination of the appropriate degrees of freedom in the asymptotic chi-square distribution. The behavior of the test under H-0 and for selected alternatives is investigated by Monte Carlo simulation. The test is applied to investigate the dependence structure of daily German asset returns. It turns out that the Gauss copula is inappropriate to describe the dependencies in the data. A t(v)-copula with low degrees of freedom performs better.