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

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.

Keywords:

• Factor model
• principal component
• structural change
• test

JEL CLASSIFICATION:

• C12
• C38

Acknowledgments

I am grateful to the editor Esfandiar Maasoumi, an associate editor and two anonymous referees for their constructive suggestions and comments. I also thank Valentina Corradi, Kunpeng Li, Bent Nielsen, Kevin Sheppard, James Stock, James Wolter and the conference and seminar participants at the Panel Data Conference 2015 (Budapest), the Conference on Frontiers of Theoretical Econometrics (Konstanz), the 2016 Asian Meeting of the Econometric Society (Kyoto), University of Oxford, Lancaster University and Capital University of Economics and Business for their helpful comments.

Notes

1 Other popular kernel functions can also be used.

2 The data set is downloadable from Professor Mark W. Watson’s personal website https://www.princeton.edu/∼mwatson/

3 Known from Tables 1 and 2, the critical value of the aggregate test statistic for $N=109,r=2$ corresponding to the 0.01 significance level is between 1.97 and 2.09 or between 2.13 and 2.15.