On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression

Аннотация

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 ω² type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under local alternatives.