Estimation and inference of change points in high-dimensional factor models

Economics

Jushan Bai, Xu Han, Yutang Shi

Published in Journal of Econometrics, November 2020

High-dimensional factor models are powerful tools to analyze the common driving force of a large number of variables in economics and finance. These models are usually estimated under the assumption that the parameters in the model are stable over time. This assumption is likely to be violated in practice.

Dr Xu Han Associate Professor, Department of Economics and Finance and co-authors are interested in the setup where the factor loading coefficients change at a certain point of time, which is the so-called structural break. Once practitioners know the existence of a break in the model, the next question of interest is to find the date of the break.  

“We show that the location of the break point can be accurately estimated under both large and small breaks, though in general, it is more difficult to locate the break point when the magnitude of the break is smaller,” says Han.

Han and co-authors contribute to the literature by proving that break point can be correctly estimated in large samples under much smaller breaks than those considered in the previous studies. This new result is due to the large cross-sectional dimension of the data, where the co-movement driven by the latent factors helps detecting the location of the break point.  

Their second major contribution is that they establish the asymptotic distribution of the estimated break point. Unlike existing studies in the literature, their result can characterize the estimation uncertainty of the estimator in finite samples.

“We show that the distribution of the estimated break date depends on the generating processes of the unobserved factors. Thus, a bootstrap procedure is developed to construct confidence intervals for the estimated break date,” Han added.