Approximate Factor Models with Weaker Loadings

• Tác giả: Jushan Bai, Serena Ng
• Ngôn ngữ: eng
• Ký hiệu phân loại: 511.4 Approximations formerly also 513.24 and expansions
• Thông tin xuất bản: 2021
• Bộ sưu tập: Metadata
• ID: 167779

Tóm tắt

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is positive definite in the limit when $\alpha=1$, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when $\alpha\in(0,1]$ albeit at slower rates and under additional assumptions on the sample size. The results hold whether $\alpha$ is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.