Evaluating the Predictive Abilities of Semiparametric Multivariate Models

We propose a new semiparametric procedure for estimating multivariate models with conditioning variables. The semiparametric model is based on the parametric conditional copula and nonparametric conditional marginals. To avoid the curse of dimensionality in the estimation of the latter, we propose a dimension reduction technique. The marginals are estimated using conditional kernel smoothers based on local linear estimator. The semiparametric copula model is compared with the parametric DCC model using predictive likelihood as a criterion. The comparison is based on the recent conditional test for predictive abilities. We use various simulations and financial series to compare the methods and show when the proposed semiparametric model is expected to be superior to the fully parametric DCC model