Abstract

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two-step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the first step and a CUSUM (cumulative sum) refinement step on an aggregated time series in the second step. Thus, for a fixed time-point, we can capture both the biggest break across different coordinates and aggregating simultaneous breaks over multiple coordinates. Extending the existing high-dimensional Gaussian approximation theorem to dependent data with jumps, the theory allows us to characterize the size and power of our multiple change-point test asymptotically. Moreover, we can make inferences on the breakpoints estimates when the break sizes are small. Our theoretical setup incorporates both weak temporal and strong or weak cross-sectional dependence and is suitable for heavy-tailed innovations. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the U.S. unemployment rate is considered to illustrate the usefulness of our method.

摘要

对于高维时间序列的多变点检测，我们提供了关于断点统计和估计断点大小的一致性和渐近分布的渐近理论。该理论支持一个简单的两步程序来检测和估计多个变化点。所提出的两步过程涉及第一步中的 MOSUM（移动和）类型统计数据的最大值，以及第二步中聚合时间序列的 CUSUM（累积和）细化步骤。因此，对于一个固定的时间点，我们可以捕获不同坐标上的最大中断和多个坐标上的同时中断的聚合。将现有的高维高斯逼近定理扩展到具有跳跃的相关数据，该理论使我们能够渐进地表征多变点测试的大小和功效。此外，当断点尺寸较小时，我们可以对断点估计进行推断。我们的理论设置结合了弱时间和强或弱的横截面依赖性，适用于重尾创新。提出了一种鲁棒的长期协方差矩阵估计，它可以是独立的兴趣。一个检测美国失业率结构变化的应用被认为可以说明我们方法的有用性。提出了一种鲁棒的长期协方差矩阵估计，它可以是独立的兴趣。一个检测美国失业率结构变化的应用被认为可以说明我们方法的有用性。提出了一种鲁棒的长期协方差矩阵估计，它可以是独立的兴趣。一个检测美国失业率结构变化的应用被认为可以说明我们方法的有用性。