Local Power of Tests of Fit for Normality of 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 and ${\omega }^2$ type is constructed for testing hypotheses on the normality of innovations. We obtain the asymptotic power of these tests under local alternatives.