Title: A non-parametric cusum-type test for testing relevant change in copulas
Authors: Tim Kutzker - University of Cologne (Germany) [presenting]
Florian Stark - University of Cologne (Germany)
Dominik Wied - University of Cologne (Germany)
Abstract: A new non-parametric test is proposed for detecting relevant breaks in copula functions. The hypothesis is of the form $H_0:|| C_1(u)-C_2(u)||\leq \Delta$ versus $H_1:|| C_1(u)-C_2(u)|| > \Delta$, where $\Delta$ is an adjustable size to allow for difference in the copulas $C_1$ and $C_2$. The test is based on suitable differences between empirical copulas and it is shown that the test statistic is asymptotically normally distributed when the marginals are known. Critical values are determined by bootstrap approximations. In the case of known marginals, it is sufficient to bootstrap the variance, while we bootstrap the whole testing process in the case of unknown marginals. We analyze the behavior of the test in Monte Carlo simulations and a real data application.