Structural Change Detection in High-Dimensional Transformed Factor Models via Canonical Correlation Analysis

Abstract: This paper develops a canonical-correlation-based method for detecting structural changes in high-dimensional transformed factor models. The proposed approach exploits the low-rank canonical-correlation structure induced by dynamically dependent common factors, while serially uncorrelated idiosyncratic components correspond to a noise subspace with zero canonical correlations. We construct an eigenvalue-ratio criterion that measures residual dynamic dependence in the estimated noise subspace and identifies the true change point under sufficient separation of the regime-specific loading spaces or dynamic canonical correlation structures. Since the change-point location and the regime-specific factor numbers are both unknown, we further propose an alternating iterative estimation procedure that updates them sequentially until convergence. Under suitable mixing and moment conditions, we establish asymptotic properties of the proposed estimators, with convergence rates depending explicitly on factor strength, cross-sectional dimension, and sample size. Monte Carlo experiments and empirical applications to intraday stock returns and U.S. temperature series demonstrate the finite-sample