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Combination Test for Mean Shift and Variance Change Gao, Min; Shi, Xiaoping; Wang, Xuejun; Yang, Wenzhi

Abstract

This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.

Item Metadata

Title
Combination Test for Mean Shift and Variance Change
Creator
Gao, Min; Shi, Xiaoping; Wang, Xuejun; Yang, Wenzhi
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2023-10-25
Description
This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.
Subject
change-point of mean; change-point of variance; CUSUM estimator; limit distribution; mixing sequences
Genre
Article
Type
Text
Language
eng
Date Available
2023-11-27
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0437891
URI
http://hdl.handle.net/2429/86680
Affiliation
Science, Irving K. Barber Faculty of (Okanagan); Non UBC; Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Citation
Symmetry 15 (11): 1975 (2023)
Publisher DOI
10.3390/sym15111975
Peer Review Status
Reviewed
Scholarly Level
Faculty; Researcher
Rights URI
https://creativecommons.org/licenses/by/4.0/
Aggregated Source Repository
DSpace

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CC BY 4.0