Work

M-procedures robust to structural changes detection under strong mixing heavy-tailed time series models

Year: 2025

Type: article

Abstract: Many tests of change points resort to least squares estimation method, but it can lead to bias if these observations are heavy-tailed processes. The aim of this paper is to construct a ratio-typed test based on M-estimation, which avoids the long-range variance estimation and is robust to structural change detection under strong mixing series with heavy-tailed. The proposed test consisting of M-procedures has more utility in that it allows processes in the domain of attraction of a stable law with index κ ∈ ( 0 , 2 ) , not limited to ( 1 , 2 ) . Under some regular conditions, asymptotic distribution under the null hypothesis of no change is functional of a Brownian motion, and the divergent rate under the alternative hypothesis is also provided. Furthermore, the convergence rate of a ratio-typed change point estimator is established. Simulation study illustrates there is no distortion in empirical sizes, and empirical powers have satisfactory performance. Finally, two practical applications to real examples are presented as well.

Source: Journal of Statistical Planning and Inference

DOI: 10.1016/j.jspi.2025.106295

Authors: Hao Jin, Jiating Hu, Ling Zhu, Shiyu Tian, Si Zhang

Institutions: Xi'an University of Science and Technology, Chongqing College of Mobile Communication

Language: English

Topic: Advanced Statistical Process Monitoring

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, National Natural Science Foundation of China, Natural Science Foundation of Shaanxi Province, Department of Human Resources and Social Security of Shaanxi Province