Local power of Kolmogorov’s and omega-squared type criteria in autoregression

A stationary $AR(p)$ model is considered. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parametric estimates, an analog of the empirical distribution function is defined and tests of Kolmogorov's and $\omega^2$ type are constructed for testing hypotheses on the distribution of innovations. The asymptotic power of these tests under local alternatives is obtained.