OPTIMAL CHANGE-POINT ESTIMATION IN TIME SERIES

• 成果类型: Article
• 署名作者: Chan, Ngai Hang; Ng, Wai Leong; Yau, Chun Yip; Yu, Haihan
• 署名单位: Chinese University of Hong Kong; Hang Seng University of Hong Kong; Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2039
• 发表日期: 2021
• 页码: 2336-2355
• 关键词: Bootstrap; GARCH; calibration

摘要

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under alpha-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.