Title: Goodness-of-fit test for innovation copula in multivariate nonparametric time series
Authors: Sarka Hudecova - Charles University, Prague (Czech Republic) [presenting]
Natalie Neumeyer - University of Hamburg (Germany)
Marek Omelka - Charles University (Czech Republic)
Abstract: Copula-based models have become popular for modelling multivariate econometric time series. Within these applications, the multivariate models are usually built from univariate models via a copula function and the conditional version of Sklar's theorem. The whole model has three separate components: conditional model (conditional mean and conditional variance), marginal distributions of innovations, and the innovation copula. We consider nonparametric estimation of the conditional model and the marginal distributions of the innovations. For the estimation of the innovation copula, both nonparametric and parametric estimators based on the estimated residuals are considered. We show that under some regularity assumptions, these copula estimators are asymptotically equivalent to estimators that would be based on the unobserved innovations, i.e. the asymptotic distribution is not affected by the necessary pre-estimation of the mean and variance functions. Furthermore, we propose a goodness-of-fit test for correct specification of the innovation copula, which is based on a comparison between the parametric and nonparametric copula estimator.