Eigenvalue tests for the number of latent factors in short panels

Alain-Philippe Fortin, Patrick Gagliardini and Olivier Scaillet
Additional contact information
Alain-Philippe Fortin: HEC Montreal
Patrick Gagliardini: University of Lugano; Swiss Finance Institute

No 22-81, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 an 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.

Pages: 67 pages
Date: 2022-10
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Citations: View citations in EconPapers (1)

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Related works:
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:chf:rpseri:rp2281

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