Taxonomy and Estimation of Multiple Breakpoints in High-Dimensional Factor Models*

This paper proposes a quasi-maximum likelihood (QML) estimator for break points in high-dimensional factor models, specifically accounting for multiple structural breaks. We begin by establishing a necessary and sufficient condition to categorize two distinct types of breaks in factor loadings: singular changes and rotational changes. The analysis of the nearly singular subsample covariance matrices of the pseudo-factors plays a key role in our approach. It allows us to demonstrate that the QML estimator precisely identifies the true breakpoint with probability tending to one for singular changes. For rotational changes, we demonstrate that the estimator exhibits stochastically bounded estimation errors, implying break fraction consistency. Furthermore, we introduce an information criterion to estimate the number of breaks, proving that it can detect the true number with probability tending to one. Monte Carlo simulations confirm the strong finite sample performance of our proposed methods. Finally, we provide an empirical example to estimate structural breakpoints in the FRED-MD dataset spanning 1959 to 2024.