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

Alain-Philippe Fortin, Patrick Gagliardini and Olivier Scaillet
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Alain-Philippe Fortin: University of Geneva
Patrick Gagliardini: University of Lugano; Swiss Finance Institute

No 25-27, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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.

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 (search for similar items in EconPapers)
JEL-codes: C12 C23 C38 C58 G12 (search for similar items in EconPapers)
Pages: 69 pages
Date: 2025-03
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2527

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