A1749
Title: Inference for change-points in time series under various break sizes
Authors: Chun Yip Yau - Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: The asymptotic distribution of a change-point estimator for piecewise stationary time series is investigated across different magnitudes of break sizes. Specifically, break sizes of order $O(1/n^\alpha)$ for $0 < \alpha < 1/2$, $= 1/2$, and $> 1/2$ are examined, corresponding to large, moderate, and small break sizes, respectively, where $n$ denotes the sample size. Results reveal that the asymptotic distributions in these three regimes differ but are all linked to the maximizer of certain functions of a two-sided drifted Brownian motion. To address the practical challenge of unknown break sizes, an asymptotically pivotal statistic is introduced that is robust across the whole range of break size regimes on $[0,\infty)$. This statistic provides a unified approach for constructing confidence intervals for the change-point without requiring prior knowledge of the break size. Simulation studies show that the asymptotic inference performs well under different break sizes, while the pivotal statistic demonstrates better performance in most scenarios. Applications to financial time series further highlight the practical relevance of the proposed inference methods.
