Testing the Number of Common Factors by Bootstrapped Sample Covariance Matrix in High-Dimensional Factor Models

• 成果类型: Article
• 署名作者: Yu, Long; Zhao, Peng; Zhou, Wang
• 署名单位: Shanghai University of Finance & Economics; Jiangsu Normal University; Jiangsu Normal University; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2346364
• 发表日期: 2025
• 页码: 448-459
• 关键词: dynamic-factor-model; spectral statistics; EIGENVALUE; identification; limit

摘要

This article studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.