Robust ratio-typed test for location change under strong mixing heavy-tailed time series model

Hao Jin, Shiyu Tian, Jiating Hu, Ling Zhu and Si Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 18, 5760-5783

Abstract: The data distributions of many financial and econometric sequences always exhibit heavy-tailed phenomena, which trigger distinct difficulty in parameter estimation by classical least squares method. This article aims to construct a new ratio-typed test based on least absolute deviation estimation that effectively circumvents the problem of long-run variance estimation and has robustness on detecting structural changes under strong mixing sequences with heavy-tailed innovations. This is because the least absolute deviation estimation can allow for processes within the domain of attraction of a stable law with an index κ∈(0,2), not limited to (1, 2). Under some regular conditions, the asymptotic distribution under the null hypothesis is derived as a functional of Brownian motion, not a functional of lévy process, and the divergence rate under the alternative hypothesis is also provided. Furthermore, the consistency of a ratio-typed change point estimator is given and its convergence rate is established. The numerical simulation indicates that empirical sizes are undistorted, and empirical powers exhibit significant performance. Finally, two practical application examples are presented to illustrate the validity of the proposed test procedures.

Date: 2025
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DOI: 10.1080/03610926.2024.2446396

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