On the Local Power of Kolmogorov-Smirnov's and Pearson's Tests in Autoregression

We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov's, $\omega^2$ and Pearson's type is constructed for testing hypotheses on the disnribution of innovations. We obtain the asymptotic power of these tests under local alternatives.
The AR(p) model with gross errors in the observations is also considered