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August 2021 Optimal change-point estimation in time series
Ngai Hang Chan, Wai Leong Ng, Chun Yip Yau, Haihan Yu
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Ann. Statist. 49(4): 2336-2355 (August 2021). DOI: 10.1214/20-AOS2039

Abstract

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real data applications are presented to investigate the finite sample performance of the Bayes-type estimator and the bootstrap procedures.

Funding Statement

Research supported in part by grants from HKSAR-RGC-GRF Nos. 14308218 and HKSAR-RGC-TRF No. T32-101/15-R (Chan), HKSAR-RGC-GRF Nos. 14302719 and 14305517 (Yau), and HKSAR-RGC-FDS No. UGC/FDS14/P01/20 (Ng).

Acknowledgments

We would like to thank the Coeditor, an Associate Editor and the anonymous referees for their critical comments and thoughtful suggestions, which lead to a much improved version of this paper.

Citation

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Ngai Hang Chan. Wai Leong Ng. Chun Yip Yau. Haihan Yu. "Optimal change-point estimation in time series." Ann. Statist. 49 (4) 2336 - 2355, August 2021. https://doi.org/10.1214/20-AOS2039

Information

Received: 1 April 2018; Revised: 1 October 2020; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/20-AOS2039

Subjects:
Primary: 62M10
Secondary: 60F25

Keywords: Bayes-type estimator , Confidence interval , double-sided random process , piecewise stationary time series , structural break

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • August 2021
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