Bayesian Estimation of the Eigenstructure in High-Dimensional Approximate Factor Models

2026-06-23

AI Summary

This study addresses the instability of principal component-based estimation in high-dimensional approximate factor models, where the number of variables far exceeds the sample size, leading to severe distortion in the eigenstructure of the sample covariance matrix. The paper presents the first systematic application of a Bayesian framework to this problem, enabling joint posterior inference of factor loadings and latent factors. Theoretically, the proposed approach achieves a posterior contraction rate comparable to the benchmark established for high-dimensional spiked covariance models. Simulation studies demonstrate that the method more accurately recovers the underlying factor structure. In empirical applications to macro-financial data, the estimated factors exhibit clear economic interpretability and significantly outperform existing methods in predictive tasks.

Abstract

High-dimensional economic datasets often display strong co-movement driven by a small number of latent factors, which are typically modeled using approximate factor models. When the number of variables is large relative to the sample size, the eigenvalues and eigenvectors of the sample covariance matrix are severely distorted, which in turn makes principal component based estimators of the factor structure unstable. To address the high-dimensional problem, we propose a Bayesian model for approximate factor structures. We show that the posterior convergence rate is of the same order as benchmark results for high-dimensional spiked covariance models. Simulation studies show that the proposed method more accurately recovers the factor structure in approximate factor models than existing methods. Real data analyses on macro--financial datasets illustrate that the proposed method provides interpretable estimates of latent factor structure and performs competitively in forecasting exercises.

Problem

• high-dimensional
• approximate factor models
• eigenstructure
• spiked covariance
• latent factors

Innovation

• Bayesian estimation
• high-dimensional factor models
• eigenstructure recovery
• spiked covariance
• posterior convergence rate