Optimal change-point estimation in time series
Ngai Hang Chan, Wai Leong Ng, Chun Yip Yau, Haihan Yu
The Annals of Statistics · 2021 · Volume 49 · Issue 4
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.
Keywords
60F25, 62M10, Bayes-type estimator, Confidence interval, double-sided random process, piecewise stationary time series, structural break
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