A0236
Title: Change point inference in high-dimensional regression models under temporal dependence
Authors: Daren Wang - Notre Dame (United States) [presenting]
Haotian Xu - University of Warwick (United Kingdom)
Zifeng Zhao - Notre Dame (United States)
Yi Yu - University of Cambridge (United Kingdom)
Abstract: The focus is on the limiting distributions of change point estimators in a high-dimensional linear regression time series context, where a regression object is observed at every time point. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in $L_2$-norm. Limiting distributions of the change point estimators are provided in the regimes where the minimal jump size vanishes and where it remains constant. Both the covariate and noise sequences are temporally dependent in the functional dependence framework, which is the first time seen in the change point inference literature. A block-type long-run variance estimator is shown to be consistent under functional dependence, which facilitates the practical implementation of the derived limiting distributions. A few important byproducts of the analysis are also presented, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost computational efficiency, consistent change point localization rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support the theoretical results.
