Theory of Probability &Its Applications, Volume 65, Issue 1, Page 102-110, January 2020.
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.

中文翻译：

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关于离群值的自回归正态性的皮尔逊卡方检验

概率论及其应用，第65卷，第1期，第102-110页，2020年1月。
我们考虑具有观测值的线性线性\ operatorname {AR}（p）$模型，该观测值会受到严重误差（异常值）的影响。自回归参数和创新分布是未知的。基于参数估计量的残差，我们构造了经验分布函数的类似物以及相应的Pearson卡方检验，以检验创新分布的正态性（我们记得，创新的正态性等于自回归序列的正态性本身）。我们还找到了局部替代项下测试的渐近能力，并在假设和替代项下建立了测试的定性鲁棒性。