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-particularly cryptocurrencies-are notoriously unstable. Empirical evidence indicates that these covariance structures often exhibit power-law scaling, reflecting complex and hierarchical interactions among assets. Building on this insight, we propose a power-law covariance model to characterize the collective dynamics of cryptocurrencies and develop a hybrid estimator that integrates Random Matrix Theory (RMT) with Residual Neural Networks (ResNets). The RMT component regularizes the eigenvalue spectrum under high-dimensional noise, while the ResNet learns data-driven corrections to recover latent structural dependencies. Monte Carlo simulations show that ResNet-based estimators consistently minimize both Frobenius and minimum-variance (MV) losses across diverse covariance models. Empirical experiments on 89 cryptocurrencies (2020-2025), using a training period ending at the local BTC maximum in November 2021 and testing through the subsequent bear market, demonstrate that a two-step estimator combining hierarchical filtering with ResNet corrections yields the most profitable and balanced portfolios, remaining robust under market regime shifts. These findings highlight the potential of combining RMT, deep learning, and power-law modeling to capture the intrinsic complexity of financial systems and enhance portfolio optimization under realistic conditions.