Testing common structure in high-dimensional factor models: change-point and two-sample procedures

Abstract

This work proposes a novel procedure to test for common structures across two high-dimensional factor models. The introduced test allows to uncover whether two factor models are driven by the same loading matrix up to some linear transformation. The test can be used to discover inter-individual relationships between two datasets. In addition, it can be applied to test for structural changes over time in the loading matrix of an individual factor model. The test aims to reduce the set of possible alternatives in a classical change-point setting. The theoretical results establish the asymptotic behavior of the introduced test statistic. The theory is supported by a simulation study showing promising results in empirical test size and power. Two real data applications are considered: the first investigates changes in the loadings of the celebrated US macroeconomic dataset of Stock and Watson, and the second examines similarities of the loadings of macroeconomic indicators for the US and South Korea.