基于稀疏张量分解的高维时间序列谱变点估计

主讲人：张心雨

张心雨，华东师范大学统计学院准聘副教授。2017年本科毕业于中国人民大学统计学院，2022年毕业于清华大学获统计学博士学位，之后在美国爱荷华大学从事博士后研究。主要研究方向包括高维统计推断、时间序列分析、变点检测和谱分析等，同时也涉及神经影像数据分析与慢性肺病研究。研究成果已接收发表于 JRSSB、JBES、JRSSA 等统计学与计量经济学权威期刊。

1  报告信息

时间 

2025年10月16日（周四）

14:00-15:00

地点 

中国人民大学

明德主楼1016会议室

2  报告摘要

Multivariate time series may be subject to partial structural changes over certain frequency band, for instance, in neuroscience. We study the change point detection problem with high dimensional time series, within the framework of frequency domain. The overarching goal is to locate all change points and delineate which series are activated by the change, over which frequencies. In practice, the number of activated series per change and frequency could span from a few to full participation. We solve the problem by first computing a CUSUM tensor based on spectra estimated from blocks of the time series. A frequency-specific projection approach is applied for dimension reduction. The projection direction is estimated by a proposed tensor decomposition algorithm that adjusts to the sparsity level of changes. Finally, the projected CUSUM vectors across frequencies are aggregated for change point detection. We provide theoretical guarantees on the number of estimated change points and the convergence rate of their locations. We derive error bounds for the estimated projection direction for identifying the frequency-specific series activated in a change. We provide data-driven rules for the choice of parameters. The efficacy of the proposed method is illustrated by simulation, as wells as applications in stock returns and seizure detection.

“统计大讲堂”由中国人民大学统计学院与应用统计科学研究中心联合主办，旨在搭建学界与业界的交流平台，促进统计理论与实践的深度融合，推动统计学科研创新，服务国家经济社会发展。作为统计学院人才培养体系的核心组成部分，“统计大讲堂”通过系列学术讲座、专题研讨等形式，为统计学子提供前沿知识传授与学术思维训练，营造开放包容的学术氛围，以培养具有国际视野、创新能力和实践精神的复合型统计人才。