论文标题
$ \ ell^2 $推论高维时间序列中的变更点通过双向Mosum
$\ell^2$ Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM
论文作者
论文摘要
我们提出了一种用于检测高维时间序列中多个变更点的推理方法，以致密或空间群集信号为目标。我们的方法通过$ \ ell^2 $ norm在横截面上汇总的统计量（MOSUM）统计数据，并随着时间的推移最大化它们。我们进一步介绍了一种新型的双向Mosum，它利用时空移动区域来寻找断裂，并在仅在几组中发生断裂时增强测试能力的额外优势。 $ \ ell^2 $ - 聚集的统计量的限制分布是通过将高维高斯定理扩展到时空非平稳过程来测试中断存在的。模拟研究表现出我们的测试表现出令人鼓舞的表现，以检测非SPARSE弱信号。在美国分析股权回报和COVID-19案件的两种应用，展示了我们提出的算法的现实世界中的相关性。
We propose an inference method for detecting multiple change points in high-dimensional time series, targeting dense or spatially clustered signals. Our method aggregates moving sum (MOSUM) statistics cross-sectionally by an $\ell^2$-norm and maximizes them over time. We further introduce a novel Two-Way MOSUM, which utilizes spatial-temporal moving regions to search for breaks, with the added advantage of enhancing testing power when breaks occur in only a few groups. The limiting distribution of an $\ell^2$-aggregated statistic is established for testing break existence by extending a high-dimensional Gaussian approximation theorem to spatial-temporal non-stationary processes. Simulation studies exhibit promising performance of our test in detecting non-sparse weak signals. Two applications, analyzing equity returns and COVID-19 cases in the United States, showcase the real-world relevance of our proposed algorithms.
