  We consider a nonparametric autoregression model under conditional
heteroscedasticity with the aim to test whether the innovation distribution
changes in time. To this end we develop an asymptotic expansion for the
sequential empirical process of nonparametrically estimated innovations
(residuals). We suggest a Kolmogorov-Smirnov statistic based on the difference
of the estimated innovation distributions built from the first ns and the last
n-ns residuals, respectively. Weak convergence of the underlying stochastic
process to a Gaussian process is proved under the null hypothesis of no change
point. The result implies that the test is asymptotically distribution-free.
Consistency against fixed alternatives is shown. The small sample performances
of the proposed test is investigated in a simulation study and the test is
applied to data examples.
