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An empirical comparison of the CUSUM and the FLSA for change points detection
Journal of the Korean Data & Information Science Society 2021;32:1317-28
Published online November 30, 2021;  https://doi.org/10.7465/jkdi.2021.32.6.1317
© 2021 Korean Data and Information Science Society.

Garyeong Lee1 · Won Son2 · Sungim Lee3 · Donghyeon Yu4

123Department of Applied Statistics, Dankook University
4Department of Statistics, Inha University
Correspondence to: 1 Graduate student, Department of Applied Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do, 16890, Republic of Korea.
2 Assistant professor, Department of Information Statistics, Dankook University, 152, Jukjeon-ro, Sujigu, Yongin-si, Gyeonggi-do, 16890, Republic of Korea.
3Professor, Department of Information Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yonginsi, Gyeonggi-do, 16890, Republic of Korea.
4 Corresponding author: Associate professor, Department of Statistics, Inha University, 100, Inha-ro, Michuhol-gu, Incheon, 22212, Republic of Korea, E-mail: dyu@inha.ac.kr
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01048127 (Donghyeon Yu) and No. 2020R1F1A1A01051039 (Won Son)).
Received September 14, 2021; Revised October 1, 2021; Accepted October 3, 2021.
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
In this paper, we study the performance of the Cumulative Sum (CUSUM) and the Fused Lasso Signal Approximator (FLSA) for detecting change points in a mean model. The two methods are widely used for identifying change points. The CUSUM statistic is based on the cumulative sums over the two intervals separated by a candidate change point. On the other hand, the FLSA is a form of regularized method, a combination of the residual sum of squares and a total variation penalty term. Although the two methods are developed from quite a different motivation, these statistics can be expressed in very similar form. The FLSA statistics derived from the pathwise algorithm (Hoefling, 2010) and the modified FLSA statistics (Son and Lim, 2019) can be used for false change points elimination and eventually for change points detection. The modified FLSA statistics are equivalent to the CUSUM statistics divided by the standard error of the difference between the means of the neighboring two blocks. We compare the performance of these statistics in various situations and find that each method has its own advantage and disadvantage for change point detection.
Keywords : CUSUM statistic, fused LASSO signal approximator, multiple change points, pathwise algorithm.