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.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
2014053
Program Officer
Huixia Wang
Project Start
Project End
Budget Start
2020-07-15
Budget End
2023-06-30
Support Year
Fiscal Year
2020
Total Cost
$32,358
Indirect Cost
Name
University of Notre Dame
Department
Type
DUNS #
City
Notre Dame
State
IN
Country
United States
Zip Code
46556