B1536
Title: Change point inference in high-dimensional regression models under temporal dependence
Authors: Haotian Xu - University of Warwick (United Kingdom) [presenting]
Daren Wang - Carnegie Mellon University (United States)
Zifeng Zhao - University of 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 $(y_t, X_t)$ in R times $R^p$ is observed at every time point t in ${1, . . . , n}$. 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 remains constant. Both the covariate and noise sequences are allowed to be temporally dependent in the functional dependence framework, which is the first time seen in the change point inference literature. It is shown that a block-type long-run variance estimator is consistent under the 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 localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package changepoints.
