  We consider a stationary linear AR($p$) model with observations subject to
gross errors (outliers). The autoregression parameters are unknown as well as
the distribution function $G$ of innovations. The distribution of outliers
$\Pi$ is unknown and arbitrary, their intensity is $\gamma n^{-1/2}$ with an
unknown $\gamma$, $n$ is the sample size. We test the hypothesis $H_0\colon
G=G_0$ with simmetric $G_0$. We find the power of the test under local
alternatives $H_{1n}(\rho)\colon G=(1-\rho n^{-1/2})G_0+\rho n^{-1/2}H$. Our
test is the special symmetrized Pearson's type test. Namely, first of all we
estimate the autoregression parameters and then using the residuals from the
estimated autoregression we construct a kind of empirical distribution function
(e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the
autoregression innovations. We obtain a stochastic expansion of this e.d.f. and
its symmetrized variant under $H_{1n}(\rho)$ , which enables us to construct
and investigate our symmetrized test of Pearson's type for $H_0$. We establish
qualitative robustness of this test in terms of uniform equicontinuity of the
limiting power (as functions of $\gamma,\rho$ and $\Pi$) with respect to
$\gamma$ in a neighborhood of $\gamma=0$.
