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Optimal Maximin GMM Tests for Sphericity in Latent Factor Analysis of Short Panels

Author

Listed:
  • Alain-Philippe Fortin

    (University of Geneva)

  • Patrick Gagliardini

    (University of Lugano; Swiss Finance Institute)

  • O. Scaillet

    (Swiss Finance Institute - University of Geneva)

Abstract

We derive optimal maximin tests for errors sphericity in latent factor analysis of short panels. We rely on a Generalized Method of Moments setting with optimal weighting under a large cross-sectional dimension n and a fixed time series dimension T. We outline the asymptotic distributions of the estimators as well as the asymptotic maximin optimality of the Wald, Lagrange Multiplier, and Likelihood Ratio-type tests. The characterisation of optimality relies on finding the limit Gaussian experiment in strongly identified GMM models under a block-dependence structure and unobserved heterogeneity. We reject sphericity in an empirical application to a large cross-section of U.S. stocks, which casts doubt on the validity of routinely applying Principal Component Analysis to short panels of monthly financial returns.

Suggested Citation

  • Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2025. "Optimal Maximin GMM Tests for Sphericity in Latent Factor Analysis of Short Panels," Swiss Finance Institute Research Paper Series 25-27, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2527
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    More about this item

    Keywords

    Latent factor analysis; Generalized Method of Moments; maximin test; Gaussian experiment; fixed effects; panel data; sphericity; large n and fixed T asymptotics; equity returns;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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