Change-point detection for high-dimensional time series using geometric mapping†
Minji Kim1 · Changryong Baek2
12Department of Statistics, Sungkyunkwan University
Correspondence to: † This work was supported by the Basic Science Research Program from the National Research Foundation of Korea (NRF-2022R1F1A1066209).
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: crbaek@skku.edu
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: crbaek@skku.edu
Received September 20, 2023; Revised October 19, 2023; Accepted October 21, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- This paper proposes a method for applying the GeomCP algorithm proposed by Grundy et al. (2020) to high-dimensional time series data. The method is based on geometric transformation and utilizes the CUSUM statistic and Block Wild Bootstrap (BWB) for change point estimation. The GeomCP algorithm involves dimension reduction through geometric transformation and estimates change points using the PELT method. However, the PELT method tends to perform poorly on data with temporal dependence. Therefore, this study aims to propose a robust methodology for time series data with temporal dependence. The proposed methodology applies geometric transformation to reduce the computational burden for analyzing change points in high-dimensional multivariate time series data. Additionally, it utilizes the BWB method to enhance performance in finite samples. Through simulation experiments, the proposed methodologies generally demonstrate superior performance in terms of size and power, as well as good predictive performance. In empirical data analysis, the methods successfully detect change points in the stock price indices of major stocks corresponding to the KOSPI 100, reflecting real economic issues.
- Keywords : Change-point, CUSUM, geometric mapping, high-dimensional time series, PELT.
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