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.

中文翻译：

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自回归中局部替代项下拟合检验的渐近性

我们考虑一个固定的AR（p）模型。自回归参数以及创新的分布都是未知的。基于从参数估计残差，经验分布函数的模拟的定义和Kolmogorov的的测试和ω ²型构造用于在创新的分布假设检验。我们在局部替代下获得了这些检验的渐近能力。