Physics-informed singular-value learning for cross-covariances forecasting in financial markets

Efstratios Manolakis, Christian Bongiorno () and Rosario Mantegna
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Efstratios Manolakis: Unict - Università degli studi di Catania = University of Catania
Christian Bongiorno: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay
Rosario Mantegna: DiFC - Dipartimento di Fisica e Chimica [Palermo] - UNIPA - Università degli studi di Palermo - University of Palermo

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Abstract: Recent advances in nonlinear shrinkage yield asymptotically optimal cleaners for large covariance matrices and have been extended to empirical cross-covariances via singular-value shrinkage. However, these approaches rely on stationarity and bounded-spectrum assumptions that are violated by real equity returns, which exhibit dependence drift and macroscopic common modes. We propose a physics-informed neural estimator that parameterizes the cleaned cross-covariance matrix in the empirical singular-vector basis and learns a nonlinear map from empirical singular values and marginal projections to cleaned singular values, recovering the cleaning performances of the analytical solution as a limiting case. On U.S. equity data, the learned correction not only improves out-of-sample cross-covariance prediction but also translates these statistical gains into better tracking-error minimization for portfolio replication. Furthermore, it remains stable in regimes where the analytical cross-covariance estimation deteriorates with universe size, suggesting an interpolation between sample-size denoising and a learned forecast correction under non-stationary dependence.

Date: 2026-11
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Published in Finance Research Letters, 2026, 110, pp.110602. ⟨10.1016/j.frl.2026.110602⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05724585

DOI: 10.1016/j.frl.2026.110602

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