Block wild bootstrap for self-normalization based change-point detection†
Junghyun Park1 · 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 July 28, 2023; Revised August 21, 2023; Accepted August 22, 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 considers applying the block wild bootstrap (BWB) approach to self-normalization method in detecting mean changes on the time series. The performance of the BWB approach is compared with three existing methods: CUSUM with asymptotic p-value, SN with asymptotic p-value, and CUSUM with BWB. Furthermore, we examine the robustness of the BWB method by considering several block lengths. Our results show that the BWB alleviate size distortions observed in the SN method, in particular with small sample sizes and strong correlations, while maintaining reasonable powers. Also, contrary to CUSUM method, the block length for SN method is robust so that it almost free from block length selection.
- Keywords : Block wild bootstrap, change-point detection, CUSUM, self-normalization
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