Simultaneous multiple change-point and factor analysis for high-dimensional time series

TL;DR

This paper introduces a novel methodology for detecting multiple change-points in high-dimensional time series with factor models, leveraging wavelets to transform the problem and accurately identify change-points in both common and idiosyncratic components.

Contribution

It provides the first comprehensive approach to simultaneous change-point detection and factor analysis in high-dimensional time series with multiple structural breaks.

Findings

Wavelet transformation simplifies change-point detection in second-order structures.

The methodology accurately estimates the number and locations of change-points.

Simulation studies show improved detection and a spillover effect linking breaks in components.

Abstract

We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting `spillover' effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of `factors'. Our methodology is implemented in the R package {\tt factorcpt}, available from CRAN.