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This research introduces a physics-informed neural estimator to address the non-stationarity of equity returns in cross-covariance forecasting, effectively bridging sample-size denoising with learned corrections. By parameterizing cleaned matrices within an empirical singular-vector basis, the method improves out-of-sample predictions and minimizes tracking error for portfolio replication even as market universes expand. The approach demonstrates that integrating domain-specific constraints into neural architectures can yield robust statistical gains where traditional analytical solutions fail under dependence drift.
Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets
arXiv:2601.07687v3 Announce Type: replace-cross 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.
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.
Statistical Finance (q-fin.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)
G.3; G.1.3; I.2.6; J.4
arXiv:2601.07687 [q-fin.ST]
(or arXiv:2601.07687v3 [q-fin.ST] for this version)
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