用物理启发的神经网络改进金融协方差预测，提升投资组合跟踪精度。
Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets
- 在经验奇异向量基下建模协方差矩阵，学习奇异值非线性映射关系。
- 在美股市数据上提升协方差预测准确率，降低投资组合复制跟踪误差。
- 适用于非平稳市场，对大市值组合仍保持稳定，适合量化风控与资产配置场景。
近年来，非线性收缩方法在大型协方差矩阵清洗中表现优异，并通过奇异值收缩扩展至实证协方差估计。然而，这些方法依赖平稳性和有界谱假设，而真实股票收益存在依赖漂移和宏观共同模式，违背该假设。本文提出一种物理启发的神经估计器，将清洗后的协方差矩阵参数化于经验奇异向量基，学习从经验奇异值与边缘投影到清洗后奇异值的非线性映射，可恢复解析解的清洗性能作为极限情况。在美股市数据上，所学修正不仅提升了协方差的样本外预测表现，还转化为更好的投资组合复制跟踪误差最小化。此外，在样本规模增大时，其性能优于解析估计，表现出样本规模去噪与学习型预测修正之间的平滑过渡，适用于非平稳依赖环境。
原文摘要 · Abstract (English)
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.
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