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

ArXiv ID: 2510.19130 “View on arXiv”

Authors: Andres Garcia-Medina

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.

Keywords: Covariance Estimation, Random Matrix Theory, Residual Neural Networks, Power-law Scaling, Portfolio Optimization, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including Random Matrix Theory (RMT), Wishart ensembles, spiked covariance models, and deep ResNet architectures, indicating high mathematical complexity. It also demonstrates empirical rigor through Monte Carlo simulations and out-of-sample testing on real cryptocurrency data across bull and bear market regimes, evaluating portfolio performance with specific loss functions.

  flowchart TD
    A["<b>Research Goal</b><br/>Improve Covariance Estimation for Short, Noisy Financial Time Series<br/>(Power-law scaling & Hierarchical structure)"] --> B["<b>Data & Model</b><br/>Data: 89 Cryptocurrencies (2020-2025)<br/>Model: Power-law Covariance Generation"]

    B --> C["<b>Methodology Pipeline</b><br/>Hybrid ResNet + RMT Estimator"]

    C --> D["<b>Step 1: RMT Regularization</b><br/>Filter noise via eigenvalue spectrum regularization"]
    C --> E["<b>Step 2: Deep Learning Correction</b><br/>ResNet learns eigenvector corrections"]

    D & E --> F["<b>Monte Carlo Simulation</b><br/>Test on synthetic populations<br/>Loss functions: Frobenius & Minimum-variance"]

    F --> G["<b>Key Findings & Outcomes</b><br/>1. ResNet reduces estimation error<br/>2. Two-step estimator yields robust portfolios<br/>3. Detects multiscale hierarchical structure"]