We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

中文翻译：

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中等偏离单位根的核估计量的渐近理论，适用于非参数检验的渐近尺寸

我们为核密度估计器提供了新的渐近理论，当它们被应用于表现出与单位根的适度偏差的自回归过程时。这填补了现有文献中的一个空白，该文献迄今为止只考虑了几乎集成和平稳的自回归过程。这些结果可应用于非参数预测回归模型。特别是，我们证明了非参数的零拒绝概率吨测试在回归量的持续程度中得到统一控制。这为通常的非参数推理程序的有效性提供了严格的理由，即使在回归变量可能高度持久的情况下也是如此。