Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets
A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. Building on this progress, these ideas have been generalized to empirical cross-covariance matrices, whose singular-value shrinkage characterizes comovements between one set of assets and another. Existing analytical cross-covariance cleaners are derived under strong stationarity and large-sample assumptions, and they typically rely on mesoscopic regularity conditions such as bounded spectra; macroscopic common modes (e.g., a global market factor) […]