Estimation and Inference of Structural Changes in High Dimensional Factor Models

This paper considers the estimation of break point in high dimensional factor models where the unobserved factors are estimated by Principal Component Analysis (PCA). The factor loading matrix is assumed to have a structural break at a certain time. We establish the conditions under which the least squares (LS) estimator is consistent for the break date. Our consistency result holds for smaller breaks than those in the existing literature. We also find the LS estimator’s asymptotic distribution, which depends on the data generating process of the unobserved factors. Simulation results confirm that the break date can be accurately estimated by the LS even if the breaks are small. In two empirical applications, we implement our method to estimate the break points in the U.S. stock market and U.S. macroeconomy, respectively.