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

TL;DR

This paper introduces a quasi-maximum likelihood estimator for detecting a single structural break in high-dimensional factor models, demonstrating its consistency and applicability through simulations and empirical data analysis.

Contribution

It proposes a novel QML estimator for break points in high-dimensional factor models that remains consistent under singular covariance matrices and rotational changes.

Findings

Estimator performs well in finite samples.

Consistent even with singular covariance matrices.

Successfully applied to macroeconomic and stock data.

Abstract

This paper estimates the break point for large-dimensional factor models with a single structural break in factor loadings at a common unknown date. First, we propose a quasi-maximum likelihood (QML) estimator of the change point based on the second moments of factors, which are estimated by principal component analysis. We show that the QML estimator performs consistently when the covariance matrix of the pre- or post-break factor loading, or both, is singular. When the loading matrix undergoes a rotational type of change while the number of factors remains constant over time, the QML estimator incurs a stochastically bounded estimation error. In this case, we establish an asymptotic distribution of the QML estimator. The simulation results validate the feasibility of this estimator when used in finite samples. In addition, we demonstrate empirical applications of the proposed method by applying it to estimate the break points in a U.S. macroeconomic dataset and a stock return dataset.