  In this paper we consider autoregressive models with conditional
autoregressive variance, including the case of homoscedastic AR-models and the
case of ARCH models. Our aim is to test the hypothesis of normality for the
innovations in a completely nonparametric way, i. e. without imposing
parametric assumptions on the conditional mean and volatility functions. To
this end the Cram\'er-von Mises test based on the empirical distribution
function of nonparametrically estimated residuals is shown to be asymptotically
distribution-free. We demonstrate its good performance for finite sample sizes
in a simulation study.
