A change-point test for autoregressive processes using a harmonic mean p-value

L. Ma; G. Sofronov

doi:10.36334/modsim.2021.A1.ma

A change-point test for autoregressive processes using a harmonic mean p-value

L. Ma, G. Sofronov^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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Abstract

In many different applications, it is important to know if time series data is generated from a single underlying mechanism or not. This problem, known as a change-point problem, can be formulated as a multiple hypotheses testing problem. In this paper, we propose a harmonic change-point test (HarmonicCPT) to identify and validate change-points in an autoregressive process. The method consists of two steps. First, we develop likelihood ratio based scan statistics on gathering the local information by comparing two adjacent sequences within each scanning window. The corresponding p-values are collected from each test. Any changes in mean, autoregressive coefficients, or variance lead to rejections of the null hypothesis that the data is generated from the same process within the scanning window. Next, we calculate a harmonic mean p-value by combining all of the tests on which the decision that whether to reject the global null hypothesis depends. The simulation study shows that the proposed scan statistic is quite sensitive to the variance change, and the harmonic mean p-value procedure is efficient in detecting the significant p-values.

Original language	English
Title of host publication	MODSIM2021, 24th International Congress on Modelling and Simulation
Editors	R. W. Vervoort, A. A. Voinov, J. P. Evans, L. Marshall
Place of Publication	Canberra
Publisher	Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ)
Pages	50-56
Number of pages	7
ISBN (Electronic)	9780987214386
DOIs	https://doi.org/10.36334/modsim.2021.A1.ma
Publication status	Published - 2021
Event	The 24th International Congress on Modelling and Simulation - Sydney, Australia Duration: 5 Dec 2021 → 10 Dec 2021 Conference number: 24th https://mssanz.org.au/modsim2021/index.html

Conference

Conference	The 24th International Congress on Modelling and Simulation
Abbreviated title	MODSIM2021
Country/Territory	Australia
City	Sydney
Period	5/12/21 → 10/12/21
Internet address	https://mssanz.org.au/modsim2021/index.html

Bibliographical note

Copyright the Author(s) and the Publisher. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Change-point test
autoregressive process
multiple testing
harmonic mean p-value

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10.36334/modsim.2021.A1.maLicence: CC BY

Publisher version (open access)Final published version, 1.43 MBLicence: CC BY

Cite this

Ma, L., & Sofronov, G. (2021). A change-point test for autoregressive processes using a harmonic mean p-value. In R. W. Vervoort, A. A. Voinov, J. P. Evans, & L. Marshall (Eds.), MODSIM2021, 24th International Congress on Modelling and Simulation (pp. 50-56). Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ). https://doi.org/10.36334/modsim.2021.A1.ma

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abstract = " In many different applications, it is important to know if time series data is generated from a single underlying mechanism or not. This problem, known as a change-point problem, can be formulated as a multiple hypotheses testing problem. In this paper, we propose a harmonic change-point test (HarmonicCPT) to identify and validate change-points in an autoregressive process. The method consists of two steps. First, we develop likelihood ratio based scan statistics on gathering the local information by comparing two adjacent sequences within each scanning window. The corresponding p-values are collected from each test. Any changes in mean, autoregressive coefficients, or variance lead to rejections of the null hypothesis that the data is generated from the same process within the scanning window. Next, we calculate a harmonic mean p-value by combining all of the tests on which the decision that whether to reject the global null hypothesis depends. The simulation study shows that the proposed scan statistic is quite sensitive to the variance change, and the harmonic mean p-value procedure is efficient in detecting the significant p-values.",

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Ma, L & Sofronov, G 2021, A change-point test for autoregressive processes using a harmonic mean p-value. in RW Vervoort, AA Voinov, JP Evans & L Marshall (eds), MODSIM2021, 24th International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ), Canberra, pp. 50-56, The 24th International Congress on Modelling and Simulation, Sydney, New South Wales, Australia, 5/12/21. https://doi.org/10.36334/modsim.2021.A1.ma

A change-point test for autoregressive processes using a harmonic mean p-value. / Ma, L.; Sofronov, G.
MODSIM2021, 24th International Congress on Modelling and Simulation. ed. / R. W. Vervoort; A. A. Voinov; J. P. Evans; L. Marshall. Canberra: Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ), 2021. p. 50-56.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AU - Sofronov, G.

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N2 - In many different applications, it is important to know if time series data is generated from a single underlying mechanism or not. This problem, known as a change-point problem, can be formulated as a multiple hypotheses testing problem. In this paper, we propose a harmonic change-point test (HarmonicCPT) to identify and validate change-points in an autoregressive process. The method consists of two steps. First, we develop likelihood ratio based scan statistics on gathering the local information by comparing two adjacent sequences within each scanning window. The corresponding p-values are collected from each test. Any changes in mean, autoregressive coefficients, or variance lead to rejections of the null hypothesis that the data is generated from the same process within the scanning window. Next, we calculate a harmonic mean p-value by combining all of the tests on which the decision that whether to reject the global null hypothesis depends. The simulation study shows that the proposed scan statistic is quite sensitive to the variance change, and the harmonic mean p-value procedure is efficient in detecting the significant p-values.

AB - In many different applications, it is important to know if time series data is generated from a single underlying mechanism or not. This problem, known as a change-point problem, can be formulated as a multiple hypotheses testing problem. In this paper, we propose a harmonic change-point test (HarmonicCPT) to identify and validate change-points in an autoregressive process. The method consists of two steps. First, we develop likelihood ratio based scan statistics on gathering the local information by comparing two adjacent sequences within each scanning window. The corresponding p-values are collected from each test. Any changes in mean, autoregressive coefficients, or variance lead to rejections of the null hypothesis that the data is generated from the same process within the scanning window. Next, we calculate a harmonic mean p-value by combining all of the tests on which the decision that whether to reject the global null hypothesis depends. The simulation study shows that the proposed scan statistic is quite sensitive to the variance change, and the harmonic mean p-value procedure is efficient in detecting the significant p-values.

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ER -

A change-point test for autoregressive processes using a harmonic mean p-value

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Keywords

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