A Randomized Sequential Procedure to Determine the Number of Factors

• 成果类型: Article
• 署名作者: Trapani, Lorenzo
• 署名单位: City St Georges, University of London
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1328359
• 发表日期: 2018
• 页码: 1341-1349
• 关键词: approximate factor models; EIGENVALUE; arbitrage; tests; limit

摘要

This article proposes a procedure to estimate the number of common factors k in a static approximate factor model. The building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge, while the others stay bounded. On the grounds of this, we propose a test for the null that the ith eigenvalue diverges, using a randomized test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions on the data, and no assumptions are required on factors, loadings or idiosyncratic errors. The randomized tests are then employed in a sequential procedure to determine k. Supplementary materials for this article are available online.