Abstract

Detection of variance change points is statistically difficult when the data

exhibit a varying mean structure and autocorrelation.

Existing variance change

point tests either require the assumption of mean constancy or sacrifice testing power

due to serial dependence. This article addresses these problems by proposing a trendrobust and autocorrelation-efficient variance change point test via a differencing

approach. This approach removes the mean effect without fitting the mean function.

It also allows the test to retrieve the reduced power due to serial dependence. We

prove that the optimal difference-based test should minimize the long-run coefficient

of variation of the sample second moment of the noises instead of the long-run

variance in the presence of serial dependence. The optimal solution can be efficiently

computed by fractional quadratic programming. The asymptotic relative efficiency

under a local alternative hypothesis is derived. A rate-optimal long-run variance

estimator is also proposed. It is proven to be doubly robust against varying mean

and variance change points.

Key words and phrases: change point, cumulative sum, difference sequence, long-run variance, non-linear time series

Information

Preprint No.SS-2023-0238
Manuscript IDSS-2023-0238
Complete AuthorsCheuk Wai Leung, Kin Wai Chan
Corresponding AuthorsKin Wai Chan
Emailskinwaichan@cuhk.edu.hk

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Acknowledgments

The authors would like to thank the anonymous referees, an associate editor, and

the editor for their constructive comments that improved the scope and presentation

of the paper. Chan thanks the partial support provided by grants GRF-14304420,

Testing for Variance Changes

14306421, and 14307922 from the Research Grants Council of HKSAR.

Supplementary Materials

It includes the extra theoretical results, additional simulation experiments and

proofs.

Supplementary materials are available for download.