A1346
Title: Asymptotic inference for change-points in time series
Authors: Xinyi Tang - The Hang Seng University of Hong Kong (Hong Kong) [presenting]
Abstract: The asymptotic distribution of a change-point estimator for piecewise stationary time series across different magnitudes of break sizes is investigated. Specifically, break sizes of order $O(1/n^{\alpha})$ for $0 < \alpha < 1/2$, $\alpha = 1/2$, and $\alpha > 1/2$, corresponding to large, moderate, and small break sizes, respectively, where $n$ denotes the sample size, are examined. The 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 that is robust across the whole range of break size regimes on $\alpha \in [0,\infty)$ is introduced. 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.
