A Randomized Sequential Procedure to Determine the Number of Factors

By Lorenzo Trapani. Journal of the American Statistical Association, 2018

84 citations recorded by the source corpus.

ABSTRACT 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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/30e987ae69f8261c9d03a436516561e04230a1cf

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Citations in the corpus

Principal Component Analysis of High-Frequency Data (2016, background): “Waternaux (1976) showed that a similar central limit result holds for simple eigenvalues as long as the distribution of the data has finite fourth moment, while Tyler (1981) and Eaton and Tyler (1991) obtained the asymptotic distribution of eigenvectors and eigenvalues under more general assumptions”
Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, background): “data (see, e.g., Bai and Ng, 2002; Onatski, 2010; Ahn and Horenstein, 2013; Trapani, 2017), which is not available for semimartingales.”