Testing for Structural Changes in Large Dimensional Factor Models via Discrete Fourier Transform

We propose a new test for structural changes in large dimensional factor models via a discrete Fourier transform (DFT) approach. If structural changes occur, the conventional principal component analysis fails to estimate common factors and factor loadings consistently. The estimated residuals will contain information about structural changes. Therefore, we can compare the DFT of the estimated residuals with the null (zero) spectrum implied by no structural change. The proposed test is powerful against both smooth structural changes and abrupt structural breaks with a possibly unknown number of breaks and unknown break dates in factor loadings. It can detect a class of local alternatives at the parametric rate. As a result, the test is asymptotically more efficient than the existing tests in the factor model literature. And our test is also robust to serial and cross-sectional dependence of unknown form without having to estimate any long-run variance-covariance matrix. Moreover, it is easy to implement and tuning parameter-free. Monte Carlo studies demonstrate its reasonable size and excellent power in detecting various forms of structural changes in factor loadings. In an application to the U.S. macroeconomic data, we find significant and robust evidence of time-varying factor loadings