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Eigenvalue tests for the number of latent factors in short panels

Author

Listed:
  • Alain-Philippe Fortin

    (HEC Montreal)

  • Patrick Gagliardini

    (University of Lugano; Swiss Finance Institute)

  • O. Scaillet

    (Swiss Finance Institute - University of Geneva)

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.

Suggested Citation

  • Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2281
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    Cited by:

    1. Alain-Philippe Fortin & Patrick Gagliardini & Olivier Scaillet, 2023. "Latent Factor Analysis in Short Panels," Swiss Finance Institute Research Paper Series 23-44, Swiss Finance Institute.
    2. Torben G. Andersen & Yi Ding & Viktor Todorov & Seunghyeon Yu, 2025. "The Factor Structure of Jump Risk," Working Papers 202531, University of Macau, Faculty of Business Administration.

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