Quasi-maximum likelihood estimation of break point in high-dimensional factor models

This paper proposes a quasi-maximum likelihood (QML) estimator of the break point for large-dimensional factor models with a single structural break in the factor loading matrix. We show that the QML estimator is consistent for the true break point when the covariance matrix of the pre- or post-break factor loading (or both) is singular. Consistency here means that the deviation of the estimated break date from the true break date k0 converges to zero as the sample size grows. This is a much stronger result than the break fraction ˆk/T being T-consistent (super-consistent) for k₀/T . Also, singularity occurs for most types of structural changes, except for a rotational change. Even for a rotational change, the QML estimator is still T-consistent in terms of the break fraction. Simulation results confirm the theoretical properties of our estimator, and it significantly outperforms existing estimators for change points in factor models.