Testing for time-varying factor loadings in high-dimensional factor models

Abstract

Abstract This paper proposes a test for structural changes in factor loadings in high-dimensional factor models under weak serial and cross-sectional dependence. The test is an aggregate statistic in the form of the maximum of the variable-specific statistics whose asymptotic null distribution and local power property are studied. Two approaches including extreme value theory and Bonferroni correction are adopted to compute the critical values of the aggregate test statistic. Monte Carlo simulations reveal the non-trivial power of the proposed test against various types of structural changes, including abrupt changes, nonrandom smooth changes, random-walk variations and stationary variations. Additionally, our test can be more powerful than some alternative tests in the considered scenarios. The usefulness of the test is illustrated by an empirical application to Stock and Watson’s U.S. data set.