On the pearson's chi-square test for normality of autoregression with outliers

We consider a stationary linear $\operatorname{AR}(p)$-model with observations subject to gross errors (outliers). The autoregression parameters and the distribution of innovations are unknown. Based on the residuals from the parameter estimators, we construct an analogue of an empirical distribution function and the corresponding Pearson chi-square type test for the normality of distributions of innovations (we recall that the normality of innovations is equivalent to that of the autoregression sequence itself). We find also the asymptotic power of the test under local alternatives and establish its qualitative robustness under a hypothesis and alternatives.