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A Randomized Sequential Procedure to Determine the Number of Factors

Trapani, Lorenzo


Lorenzo Trapani


© 2018, © 2018 American Statistical Association. 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.


Trapani, L. (2018). A Randomized Sequential Procedure to Determine the Number of Factors. Journal of the American Statistical Association, 113(523), 1341-1349.

Journal Article Type Article
Acceptance Date Apr 30, 2017
Online Publication Date Jun 26, 2017
Publication Date Jun 26, 2018
Deposit Date Oct 3, 2017
Publicly Available Date Dec 27, 2018
Journal Journal of the American Statistical Association
Print ISSN 0162-1459
Electronic ISSN 1537-274X
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Volume 113
Issue 523
Pages 1341-1349
Keywords Approximate factor models, Randomised tests, Number of factors
Public URL
Publisher URL
Additional Information This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 26/06/2017, available online:
Contract Date Oct 3, 2017


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