基于S-BCUSUM的回归模型系数变点在线检测
Online Detection of Regression Model Coefficient Change Points Based on S-BCUSUM
DOI: 10.12677/ORF.2023.132084, PDF,   
作者: 王继梅：贵州大学数学与统计学院，贵州 贵阳
关键词: 回归模型；变点；在线检测；S-BCUSUM；Regression Model； Change Point； Online Detection； S-BCUSUM
摘要: 随着信息技术的发展，近年来许多领域对在线变点检测方法的需求急剧增加，在线变点检测使人们在观测到越来越多数据时能够连续检测模型是否仍然不变，这在实际数据监控中有重要的应用价值。本文提出基于S-BCUSUM (Sequential Backward Cumulative Sum)监测统计量的封闭式在线变点检测方法用于研究回归模型系数变点的在线监测问题，在一定条件下，给出监测统计量在原假设和备择假设下的渐近性质，并通过渐近分布得到拒绝阈值。模拟结果表明，所提方法能较好地控制检验水平，且有较高的功效和较短的平均运行长度。实例分析表明，所提方法能有效监测北京市PM2.5浓度与空气污染物和气象因素之间的动态关系，这为政府部门的空气质量治理工作提供一定的理论支持，具有一定的应用前景。
Abstract: With the development of information technology, the demand for online change point detection methods has increased dramatically in many fields in recent years. Online change point detec-tion enables people to sequentially the hypothesis that the model still holds as more and more data are observed. It’s widely used in data monitoring in practice. In this paper, a closed-end online change point detection method based on the sequential backward cumulative sum statistic is proposed to investigate the online detection problem for the parameter change in linear regression model. Under certain conditions, the asymptotic properties of the monitoring statistic under the null hypothesis and the alternative hypothesis are proved. In addition, rejection threshold is obtained from the asymptotic null distribution. Simulation results show that the proposed method is able to control the test level well, and has higher power and shorter average run length. The example analysis shows that the proposed method can effectively monitor the dynamic rela-tionship between PM2.5 concentration, air pollutants and meteorological factor in Beijing, which provides a certain theoretical support for the government’s air quality control work and has certain application prospects.
文章引用：王继梅. 基于S-BCUSUM的回归模型系数变点在线检测[J]. 运筹与模糊学, 2023, 13(2): 818-831. https://doi.org/10.12677/ORF.2023.132084

参考文献

[1] Page, E.S. (1954) Continuous Inspection Schemes. Biometrika, 41, 100-115. [Google Scholar] [CrossRef] 
[2] Truong, C., Oudre, L. and Vayatis, N. (2020) Selective Review of Offline Change Point Detection Methods. Signal Processing, 167, Article ID: 107299. [Google Scholar] [CrossRef] 
[3] Aminikhanghahi, S. and Cook, D.J. (2017) A Survey of Methods for Time Series Change Point Detection. Knowledge and Information Systems, 51, 339-367. [Google Scholar] [CrossRef] [PubMed]
[4] Shi, X., Gallagher, C., Lund, R., et al. (2022) A Comparison of Single and Multiple Changepoint Techniques for Time Series Data. Computational Statistics & Data Analysis, 170, Article ID: 107433. [Google Scholar] [CrossRef] 
[5] 陈希孺. 变点统计分析简介[J]. 数理统计与管理, 1991, 10(1): 55-58.
[6] Wang, C.S.H. and Xie, Y.M. (2015) Structural Change and Monitoring Tests. In: Lee, CF. and Lee, J., Eds., Handbook of Financial Econometrics and Statistics, Springer, New York, 873-902. [Google Scholar] [CrossRef] 
[7] Chu, C.S.J., Stinchcombe, M. and White, H. (1996) Monitoring Structural Change. Econometrica, 6, 1045-1065. [Google Scholar] [CrossRef] 
[8] Horváth, L., Hušková, M., Kokoszka, P. and Steinebach, J. (2004) Monitoring Changes in Linear Models. Journal of Statistical Planning and Inference, 126, 225-251. [Google Scholar] [CrossRef] 
[9] Horváth, L., Kühn, M. and Steinebach, J. (2008) On the Per-formance of the Fluctuation Test for Structural Change. Sequential Analysis, 27, 126-140. [Google Scholar] [CrossRef] 
[10] Aue, A., Horváth, L., Kühn, M., et al. (2012) On the Re-action Time of Moving Sum Detectors. Journal of Statistical Planning and Inference, 142, 2271-2288. [Google Scholar] [CrossRef] 
[11] Chen, Z. and Tian, Z. (2010) Modified Procedures for Change Point Monitoring in Linear Models. Mathematics and Computers in Simulation, 81, 62-75. [Google Scholar] [CrossRef] 
[12] Fremdt, S. (2015) Page’s Sequential Procedure for Change-Point Detection in Time Series Regression. Statistics, 49, 128-155. [Google Scholar] [CrossRef] 
[13] Kirch, C. and Weber, S. (2018) Modified Sequential Change Point Procedures Based on Estimating Functions. The Electronic Journal of Statistics, 12, 1579-1613. [Google Scholar] [CrossRef] 
[14] Dette, H. and Gösmann, J. (2020) A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters. Journal of the American Statistical Association, 115, 1361-1377. [Google Scholar] [CrossRef] 
[15] Kojadinovic, I. and Verdier, G. (2021) Nonparametric Sequential Change-Point Detection for Multivariate Time Series Based on Empirical Distribution Functions. The Electronic Journal of Statistics, 15, 773-829. [Google Scholar] [CrossRef] 
[16] Song, J. (2021) Sequential Change Point Test in the Presence of Outliers: The Density Power Divergence Based Approach. The Electronic Journal of Statistics, 15, 3504-3550. [Google Scholar] [CrossRef] 
[17] Gösmann, J., Kley, T. and Dette, H. (2021) A New Approach for Open‐End Sequential Change Point Monitoring. Journal of Time Series Analysis, 42, 63-84. [Google Scholar] [CrossRef] 
[18] Holmes, M. and Kojadinovic, I. (2021) Open-End Nonparametric Sequential Change-Point Detection Based on the Retrospective CUSUM Statistic. The Electronic Journal of Statistics, 15, 2288-2335. [Google Scholar] [CrossRef] 
[19] Phillips, P.C.B. and Durlauf, S.N. (1986) Multiple Time Series Regression with Integrated Processes. The Review of Economic Studies, 53, 473-495. [Google Scholar] [CrossRef] 
[20] Aue, A. and Horváth, L. (2004) Delay Time in Sequential Detection of Change. Statistics & Probability Letters, 67, 221-231. [Google Scholar] [CrossRef] 
[21] Aue, A., Horváth, L. and Reimherr, M.L. (2009) Delay Times of Sequential Procedures for Multiple Time Series Regression Models. Journal of Econometrics, 149, 174-190. [Google Scholar] [CrossRef] 
[22] Casini, A. and Perron, P. (2021) Continuous Record Laplace-Based Inference about the Break Date in Structural Change Models. Journal of Econometrics, 224, 3-21. [Google Scholar] [CrossRef] 
[23] Dalla, V., Giraitis, L. and Phillips, P.C.B. (2022) Robust Tests for White Noise and Cross-Correlation. Econometric Theory, 38, 913-941. [Google Scholar] [CrossRef] 

为你推荐