A Test for Trend Gradual Changes in Heavy Tailed AR (p) Sequences

Tianming Xu (), Dong Jiang, Yuesong Wei () and Chong Wang
Additional contact information
Tianming Xu: Zhejiang Gongshang University
Dong Jiang: Zhejiang Gongshang University
Yuesong Wei: Huaibei Normal University
Chong Wang: Huaibei Normal University

Statistical Papers, 2025, vol. 66, issue 1, No 5, 20 pages

Abstract: Abstract The trend change point is the point at which the trend (or slope) in time series data changes. How to detect such change point is one of the key issues in statistical analysis. This paper proposes for a new gradual change point model for time series trend terms based on the existing abrupt change point model. Secondly, inspired by existing studies, a ratio statistic is constructed for the gradual trend change point in heavy–tailed AR(p) series. The theoretical results indicate that the asymptotic distribution of the statistic under the null hypothesis is a functional of the Lévy process. Meanwhile, this paper proves its consistency under the alternative hypothesis. In addition, due to the heavy tailed characteristics of the sequence, in order to avoid estimating the tail index and reduce the impact of extreme values on the critical values of the statistic, this paper reconstructs the test statistic based on the subsampling method and compares it with the original method. It is found that the subsampling method has a significant improvement on the test power when the change point is located later. Finally, the method is applied to the change point problem of Google stock closing price, and the trend change point is successfully detected.

Keywords: Gradual change point; Heavy–tailed sequence; Subsampling; Ratio test; 62E20; 62D05 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-024-01626-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01626-1

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-024-01626-1

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().