Eigenvalue tests for the number of latent factors in short panels

Alain-Philippe Fortin, Patrick Gagliardini and Olivier Scaillet

Papers from arXiv.org

Abstract: This paper studies new tests for the number of latent factors in a large cross-sectional factor model with small time dimension. These tests are based on the eigenvalues of variance-covariance matrices of (possibly weighted) asset returns, and rely on either the assumption of spherical errors, or instrumental variables for factor betas. We establish the asymptotic distributional results using expansion theorems based on perturbation theory for symmetric matrices. Our framework accommodates semi-strong factors in the systematic components. We propose a novel statistical test for weak factors against strong or semi-strong factors. We provide an empirical application to US equity data. Evidence for a different number of latent factors according to market downturns and market upturns, is statistically ambiguous in the considered subperiods. In particular, our results contradicts the common wisdom of a single factor model in bear markets.

Date: 2022-10
New Economics Papers: this item is included in nep-ecm
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Working Paper: Eigenvalue tests for the number of latent factors in short panels (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2210.16042

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