Denoising Complex Covariance Matrices with Hybrid ResNet and Random Matrix Theory: Cryptocurrency Portfolio Applications

Abstract

Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical interactions among assets. Motivated by this observation, we introduce a power-law covariance model to characterize collective market dynamics and propose a hybrid estimator that integrates Random Matrix Theory (RMT) with deep Residual Neural Networks (ResNets). The RMT component regularizes the eigenvalue spectrum in high-dimensional noisy settings, while the ResNet learns data-driven corrections that recover latent structural dependencies encoded in the eigenvectors. Monte Carlo simulations show that the proposed ResNet-based estimators consistently minimize both Frobenius and minimum-variance losses across a range of population covariance models. Empirical experiments on 89 cryptocurrencies over the period 2020-2025, using a training window ending at the local Bitcoin peak in November 2021 and testing through the subsequent bear market, demonstrate that a two-step estimator combining hierarchical filtering with ResNet corrections produces the most profitable and well-balanced portfolios, remaining robust across market regime shifts. Beyond finance, the proposed hybrid framework applies broadly to high-dimensional systems described by low-rank deformations of Wishart ensembles, where incorporating eigenvector information enables the detection of multiscale and hierarchical structure that is inaccessible to purely eigenvalue-based methods.