Risk forecasting in (T)GARCH models with uncorrelated dependent innovations

(G)ARCH-type models are frequently used for the dynamic modelling and forecasting of risk attached to speculative asset returns. While the symmetric and conditionally Gaussian GARCH model has been generalized in a manifold of directions, model innovations are mostly presumed to stem from an underlying IID distribution. For a cross section of 18 stock market indices, we notice that (threshold) (T)GARCH-implied model innovations are likely at odds with the commonly held IID assumption. Two complementary strategies are pursued to evaluate the conditional distributions of consecutive TGARCH innovations, a non-parametric approach and a class of standardized copula distributions. Modelling higher order dependence patterns is found to improve standard TGARCH-implied conditional value-at-risk and expected shortfall out-of-sample forecasts that rely on the notion of IID innovations.