Sequential testing for structural stability in approximate factor models

TL;DR

This paper introduces a sequential testing method to detect structural changes in large approximate factor models by analyzing eigenvalues of the sample covariance matrix, with a focus on controlling false detections and accurately identifying change-points.

Contribution

It proposes a novel monitoring procedure based on eigenvalue behavior and randomization to effectively detect changes in factor models, addressing the challenge of inconsistent eigenvalue estimation under the null.

Findings

Low probability of false detections

Accurate and tight detection times for change-points

Effective monitoring scheme demonstrated through numerical evidence

Abstract

We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes. Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic, obtaining a sequence of \textit{i.i.d} statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections, and tight detection times of change-points.