Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets

Efstratios Manolakis, Christian Bongiorno and Rosario Mantegna

Papers from arXiv.org

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: 2026-01, Revised 2026-08
New Economics Papers: this item is included in nep-big
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Finance Research Letters 110 (2026) 110602

Downloads: (external link)
https://arxiv.org/pdf/2601.07687 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2601.07687

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().