Third Year Major Oral: "L2 Inference of Change-Points for High-Dimensional Time Series"

Abstract: We propose a new inference method for multiple change-point detection of high-dimensional time series. The proposed approach targets dense or clustered cross-sectional signals. An L2-aggregated statistic is adopted in the cross-sectional dimension to detect multiple mean shifts for high-dimensional dependent data. On the theory front, we develop a framework of asymptotic theory concerning the limiting distributions of the change-point test statistics under both the null and alternatives, and the consistency of the estimated break dates. The core of our theory is to extend the high-dimensional Gaussian approximation theorem to dependent data with breaks. In particular, to facilitate the inference of breaks with natural clusters in the cross-sectional dimension, we also provide asymptotic properties of the test statistics with spatially grouped structure. Our theoretical setup is fairly general which allows for an incorporation of both temporal and cross-sectional dependence. Numerical simulations demonstrate the power enhancement of our newly proposed testing method relative to other existing techniques.

Hosts: Likai Chen and Todd Kuffner