Collaborative Research: Segmentation of Time Series via Self-Normalization

协作研究：通过自我归一化对时间序列进行分割

基本信息

批准号：
2014018
负责人：
Xiaofeng Shao
金额：
$ 15万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-15 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2014018&HistoricalAwards=false
关键词：
Collaborative Research Segmentation Time Series

项目摘要

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.

该项目旨在为时间序列数据的变更点分析开发新的统计方法和理论。变更点模型在许多科学领域都有广泛的应用，包括对美国金融市场的日常动荡进行建模，以及诸如冠状病毒等传染病的每周增长率。与现有方法相比，这项研究将为灵活的变化点模型提供推断，在实际数据集展示的复杂依赖关系下，该方法将保持有效。该项目随之而来的方法将通过出版物，会议和研讨会演示以及开源软件的开发传播到相关的科学社区。首席研究人员（PIS）将共同指导博士学位。学生并让本科生参与研究，并提供高级主题课程来介绍时间序列分析中最新的技术。Time系列细分（也称为变更点估算）是统计中的基本问题之一，其中时间序列被分段分配到各个均质段中，因此每个部分都具有相同的行为。有大量文献致力于独立观察中的变化估计。但是，可以适应时间依赖的鲁棒方法和严格的理论仍然很少。由最新的自我归一化方法（SN）方法的动机，该方法是由PI之一开发的，用于结构断裂测试和时间序列中的其他推理问题，PIS将把自分量化技术推向时间序列细分。具体而言，PI将开发系统的，统一的基于SN的更改点估计方法以及（i）将分段固定时间序列分割为均匀片段的相关理论，因此在每个零件中，有限的尺寸参数是恒定的；（ii）将具有固定和弱依赖性误差的线性趋势模型分割为恒定斜率的周期。要开发的细分算法广泛适用于固定维度的时间序列数据，可以进一步扩展以涵盖高维和本地固定时间序列，并适当修改自我归一化的测试统计统计统计。这项奖项反映了NSF的法规任务，并被认为是通过基金会的知识优点和广泛的范围来评估的，并且值得通过评估来进行评估。