Collaborative Research: Segmentation of Time Series via Self-Normalization

本项目旨在发展新的统计方法和理论，用于时间序列数据的变点分析。变点模型在许多科学领域都有广泛的应用，包括模拟美国金融市场的每日波动，以及冠状病毒等传染病的每周增长率等。与现有的方法相比，本研究将提供一个灵活的范围内的变点模型，这将保持有效的复杂的依赖关系下表现出的真实的数据集的推理。该项目产生的方法将通过出版物、会议和研讨会介绍以及开发开放源码软件向有关科学界传播。主要研究者（PI）将共同指导一名博士。时间序列分割（Time Series Segmentation），又称变点估计（Change-Point Estimation），是统计学中的一个基本问题，它将时间序列分割成多个均匀的分段，使得每一个分段都具有相同的行为。有大量的文献致力于独立观测的变点估计，然而，强大的方法和严格的理论，可以容纳时间依赖性仍然是稀缺的。受自规范化（SN）方法最近取得成功的启发，该方法是由一位PI开发的，用于时间序列中的结构突变测试和其他推理问题，PI将把自规范化技术推进到时间序列分割中。具体而言，PI将开发一个系统和统一的基于SN的变点估计方法和相关理论，用于（i）将分段平稳时间序列分割为同质片段，以便在每个片段中，有限维参数是恒定的;（ii）将具有平稳和弱相关误差的线性趋势模型分割为具有恒定斜率的周期。分割算法被开发广泛适用于固定维度的时间序列数据，并可以进一步扩展到覆盖高维和本地平稳的时间序列与适当修改的自归一化测试statistics.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

This project aims to develop new statistical methodology and theory for change-point analysis of time series data. Change-point models have wide applications in many scientific areas, including modeling the daily volatility of the U.S. financial market, and the weekly growth rate of an infectious disease such as coronavirus, among others. Compared with existing methodologies, this research will provide inference for a flexible range of change point models, which will remain valid under complex dependence relationships exhibited by real datasets. The methodologies ensuing from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations, and the development of open-source software. The Principal Investigators (PIs) will jointly mentor a Ph.D. student and involve undergraduate students in the research, and offer advanced topic courses to introduce the state-of-the-art techniques in time series analysis.Time series segmentation, also known as change-point estimation, is one of the fundamental problems in statistics, where a time series is partitioned into piecewise homogeneous segments such that each piece shares the same behavior. There is a vast body of literature devoted to change-point estimation in independent observations; however, robust methodology and rigorous theory that can accommodate temporal dependence is still scarce. Motivated by the recent success of the self-normalization (SN) method, which was developed by one of the PIs for structural break testing and other inference problems in time series, the PIs will advance the self-normalization technique to time series segmentation. Specifically, the PIs will develop a systematic and unified SN-based change-point estimation methodology and the associated theory for (i) segmenting a piecewise stationary time series into homogeneous pieces so within each piece a finite dimensional parameter is constant; (ii) segmenting a linear trend model with stationary and weakly dependent errors into periods with constant slope. The segmentation algorithms to be developed are broadly applicable to fixed-dimensional time series data and can be further extended to cover high-dimensional and locally stationary time series with proper modification of the self-normalized test statistics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.