This article presents a bootstrapped p-value white noise test based on the maximum correlation, for a time series that may be weakly dependent under the null hypothesis. The time series may be prefiltered residuals. The test statistic is a normalized weighted maximum sample correlation coefficient $ \max _{1\leq h\leq \mathcal {L}_{n}}\sqrt {n}|\hat {\omega }_{n}(h)\hat {\rho }_{n}(h)|$, where $\hat {\omega }_{n}(h)$ are weights and the maximum lag $ \mathcal {L}_{n}$ increases at a rate slower than the sample size n. We only require uncorrelatedness under the null hypothesis, along with a moment contraction dependence property that includes mixing and nonmixing sequences. We show Shao’s (2011, Annals of Statistics 35, 1773–1801) dependent wild bootstrap is valid for a much larger class of processes than originally considered. It is also valid for residuals from a general class of parametric models as long as the bootstrap is applied to a first-order expansion of the sample correlation. We prove the bootstrap is asymptotically valid without exploiting extreme value theory (standard in the literature) or recent Gaussian approximation theory. Finally, we extend Escanciano and Lobato’s (2009, Journal of Econometrics 151, 140–149) automatic maximum lag selection to our setting with an unbounded lag set that ensures a consistent white noise test, and find it works extremely well in controlled experiments.

中文翻译：

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弱相关时间序列的最大相关白噪声测试

本文介绍了一个自举p基于最大相关性的值白噪声测试，用于在原假设下可能弱依赖的时间序列。时间序列可以是预过滤的残差。检验统计量是归一化加权最大样本相关系数$ \max _{1\leq h\leq \mathcal {L}_{n}}\sqrt {n}|\hat {\omega }_{n}(h)\hat {\rho }_{n} (h)|$， 在哪里$\hat {\omega }_{n}(h)$是权重和最大滞后$ \mathcal {L}_{n}$以比样本量慢的速度增加n. 我们只需要零假设下的不相关性，以及包括混合和非混合序列的矩收缩依赖属性。我们展示了邵氏 (2011,统计年鉴35, 1773–1801) 依赖的 Wild bootstrap 对比最初考虑的更大的进程类别有效。只要将 bootstrap 应用于样本相关性的一阶扩展，它对于来自一般类参数模型的残差也是有效的。我们证明 bootstrap 是渐近有效的，而无需利用极值理论（文献中的标准）或最近的高斯逼近理论。最后，我们扩展了 Escanciano 和 Lobato (2009,计量经济学杂志151, 140–149) 自动最大滞后选择到我们的设置，具有无界滞后集，确保一致的白噪声测试，并发现它在受控实验中效果非常好。