Change-point detection in panel data via double CUSUM statistic

TL;DR

This paper introduces a novel double CUSUM statistic for detecting multiple change-points in high-dimensional panel data, demonstrating its effectiveness through theoretical analysis, bootstrap methods, simulations, and real stock market data application.

Contribution

It proposes a new double CUSUM method for change-point detection that leverages cross-sectional structure and provides a bootstrap scheme for high-dimensional data.

Findings

The method detects change-points with small cross-sectional changes.

Bootstrap improves test accuracy in correlated high-dimensional data.

Empirical results outperform existing methods.

Abstract

In this paper, we consider the problem of (multiple) change-point detection in panel data. We propose the double CUSUM statistic which utilises the cross-sectional change-point structure by examining the cumulative sums of ordered CUSUMs at each point. The efficiency of the proposed change-point test is studied, which is reflected on the rate at which the cross-sectional size of a change is permitted to converge to zero while it is still detectable. Also, the consistency of the proposed change-point detection procedure based on the binary segmentation algorithm, is established in terms of both the total number and locations (in time) of the estimated change-points. Motivated by the representation properties of the Generalised Dynamic Factor Model, we propose a bootstrap procedure for test criterion selection, which accounts for both cross-sectional and within-series correlations in high-dimensional data. The empirical performance of the double CUSUM statistics, equipped with the proposed bootstrap scheme, is investigated in a comparative simulation study with the state-of-the-art. As an application, we analyse the log returns of S&P 100 component stock prices over a period of one year.