AI 中文总结
针对高维函数时间序列白噪声检验问题，开发通用误差污染框架，提出基于交叉自协方差函数的检验统计量及参数自助法，经理论推导和模拟验证，该方法有良好有限样本性能且实用。
AI 中文摘要
白噪声检验是时间序列分析中的一个基本问题。尽管近年来高维函数时间序列领域受到越来越多关注，但由于现有检验局限于单变量函数时间序列或高维标量时间序列，该问题在很大程度上仍未解决。本文为高维函数时间序列的白噪声检验开发了一个通用的误差污染框架。提出了基于交叉自协方差函数的上确界型检验统计量，并开发了参数自助法来近似其零分布。通过施加一个一般的高级条件，得到了确保大小控制的新高斯近似结果，并建立了渐近功效保证。然后将框架应用于两个具体应用：离散观测函数时间序列的白噪声检验和函数因子模型的基于残差的拟合优度检验。大量模拟表明该方法具有良好的有限样本性能，通过应用于两个真实数据集进一步说明了其实用性。
英文摘要
White noise testing is a fundamental problem in time series analysis. Yet it remains largely unsolved for high-dimensional functional time series, despite the growing attention this area has received in recent years, as existing tests are confined to either univariate functional time series or high-dimensional scalar time series. In this paper, we develop a general error-contamination framework for testing white noise in high-dimensional functional time series. We propose a supremum-type test statistic based on cross-autocovariance functions and develop a parametric bootstrap procedure to approximate its null distribution. By imposing a general high-level condition, we derive a new Gaussian approximation result that ensures size control, and establish an asymptotic power guarantee. We then apply our framework to two concrete applications: (i) white noise test for discretely observed functional time series, and (ii) residual-based goodness-of-fit test for functional factor model. For each problem, we verify the corresponding high-level condition to ensure the theoretical validity of our proposed method. Extensive simulations show that our proposed method achieves good finite-sample performance. The practical utility of our proposed method is further illustrated through applications to two real datasets.
