Subsampling ratio tests for structural changes in time series with heavy-tailed AR(p) errors

• Published in: Communications in statistics. Simulation and computation Vol. 53; no. 8; pp. 3721 - 3747
• Main Authors: Jin, Hao, Wang, Aimin, Zhang, Si, Liu, Jia
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.08.2024; Taylor & Francis Ltd
• Subjects: Algorithms; Asymptotic methods; Heavy-tailed; Ratio test; Statistical tests; Structural change; Subsampling
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2022.2111584

In this article, we consider that issues related to the mean and trend of heavy-tailed AR(p) series are possibly subject to change at most once at some unknown point in time. Under the inspiration of Shao (J. Time Ser. Anal., 2011, 32, 598-606), two ratio statistics are constructed to test whether unknown changes have occurred. It is shown that asymptotic distributions of these test statistics under the no-change null hypothesis are functional for Lévy processes and their consistencies are given under the alternative. To avoid the nuisance parameter, we provide a subsampling method that returns more accurate critical values for these tests. The validity of the subsampling algorithm is proved. A simulation study shows the subsampling-based ratio tests achieve the correct empirical sizes and comparable empirical powers in large samples. Finally, two practical applications using real data set are presented.