STATISTICAL ANALYSIS OF FACTOR MODELS OF HIGH DIMENSION

• 成果类型: Article
• 署名作者: Bai, Jushan; Li, Kunpeng
• 署名单位: Columbia University; Tsinghua University; University of International Business & Economics; Central University of Finance & Economics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS966
• 发表日期: 2012
• 页码: 436-465
• 关键词: arbitrage; estimators; number; return

摘要

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedastic-ities, which re jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.