# Factor Analysis for High-Dimensional Time Series with Change Point

## TL;DR

This paper develops methods for detecting and estimating change points in high-dimensional time series with latent factors, allowing for strong cross-sectional dependence and using self-normalization for robust testing.

## Contribution

It introduces consistent estimators for factor loadings and change points in high-dimensional series with dependence, advancing change-point analysis in complex data.

## Key findings

- Proposed estimators are consistent under strong dependence.
- Self-normalization improves change-point test robustness.
- Numerical experiments validate the methods.

## Abstract

We consider change-point latent factor models for high-dimensional time series, where a structural break may exist in the underlying factor structure. In particular, we propose consistent estimators for factor loading spaces before and after the change point, and the problem of estimating the change-point location is also considered. Compared with existing results on change-point factor analysis of high-dimensional time series, a distinguished feature of the current paper is that our results allow strong cross-sectional dependence in the noise process. To accommodate the unknown degree of cross-sectional dependence strength, we propose to use self-normalization to pivotalize the change-point test statistic. Numerical experiments including a Monte Carlo simulation study and a real data application are presented to illustrate the proposed methods.