Regularizing stock return covariance matrices via multiple testing of correlations

Richard Luger

Journal of Econometrics, 2025, vol. 248, issue C

Abstract: This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within multiple testing procedures, controlling either the traditional familywise error rate, a generalized familywise error rate, or the false discovery proportion. Subsequent shrinkage ensures that the final covariance matrix estimate is positive definite and well-conditioned while preserving the achieved sparsity. Compared to alternative estimators, this new regularization method demonstrates strong performance in simulation experiments and real portfolio optimization.

Keywords: Regularization; Multiple testing; Sign-based tests; Generalized familywise error rate; False discovery proportion (search for similar items in EconPapers)
JEL-codes: C12 C15 C58 G11 (search for similar items in EconPapers)
Date: 2025
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Working Paper: Regularizing stock return covariance matrices via multiple testing of correlations (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:248:y:2025:i:c:s030440762400099x

DOI: 10.1016/j.jeconom.2024.105753

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