DETERMINING THE NUMBER OF FACTORS FROM EMPIRICAL DISTRIBUTION OF EIGENVALUES

• 成果类型: Article
• 署名作者: Onatski, Alexei
• 署名单位: Columbia University
• 刊物名称: REVIEW OF ECONOMICS AND STATISTICS
• ISSN/ISSBN: 0034-6535
• DOI: 10.1162/REST_a_00043
• 发表日期: 2010-11
• 页码: 1004-1016
• 关键词: arbitrage; models

摘要

We develop a new estimator of the number of factors in the approximate factor models. The estimator works well even when the idiosyncratic terms are substantially correlated. It is based on the fact, established in the paper, that any finite number of the largest idiosyncratic eigenvalues of the sample covariance matrix cluster around a single point. In contrast, all the systematic eigenvalues, the number of which equals the number of factors, diverge to infinity. The estimator consistently separates the diverging eigenvalues from the cluster and counts the number of the separated eigenvalues. We consider a macroeconomic and a financial application.