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.
From: Christian Bongiorno [view email]
[v1]
Mon, 12 Jan 2026 16:18:08 UTC (1,415 KB)
[v2]
Wed, 21 Jan 2026 10:01:01 UTC (127 KB)
[v3]
Wed, 29 Jul 2026 06:41:28 UTC (123 KB)
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