Testing for structural changes in large dimensional factor models via discrete Fourier transform

Abstract

We propose a new test for structural changes in large dimensional factor models using a discrete Fourier transform (DFT) approach. When structural changes occur, the conventional principal component analysis may fail to estimate the common factors and factor loadings consistently, and the estimated residuals contain information about the structural changes. This allows us to compare the DFT of the estimated residuals weighted by the estimated common factors 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 an unknown number of breaks and unknown break dates in factor loadings. It can detect a class of local alternatives at the rate N−1/2T−1/2, where N and T are the numbers of cross-sectional units and time periods, respectively. Monte Carlo studies demonstrate that the proposed test has reasonable size and excellent power in detecting various structural changes in factor loadings. When applied to the U.S. macroeconomic data, the test reveals significant and robust evidence of time-varying factor loadings for the post-Great Moderation sample and the pre-Great Recession subsample, which the existing literature may fail to address.