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

2026-05-31

AI Summary

This study addresses the joint estimation of structural change points and the number of latent factors in high-dimensional factor models, where both quantities are unknown. The authors introduce canonical correlation analysis into this setting for the first time, proposing an eigenvalue-ratio-based detection criterion and an alternating iterative algorithm to simultaneously estimate change-point locations and the number of factors under each regime. The method exploits the low-rank canonical correlation structure induced by common factors and the zero correlation in the noise subspace for effective identification. Under mixing and moment conditions, the theoretical analysis establishes convergence rates that depend on factor strength, cross-sectional dimension, and sample size. Monte Carlo simulations and empirical applications to intraday stock returns and U.S. temperature series demonstrate the method’s strong finite-sample performance.

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

Problem

• structural change detection
• high-dimensional transformed factor models
• canonical correlation analysis
• change point
• factor models

Innovation

• canonical correlation analysis
• structural change detection
• high-dimensional factor models
• eigenvalue-ratio criterion
• alternating iterative estimation