Denoising Correlation Matrices with Random Matrix Theory

Summary

This article presents a method for reducing sampling noise in correlation matrices used by multi-symbol trading systems. It explains that estimating many pairwise relationships from a limited return window can produce unstable eigenvalues and weights. The Marchenko–Pastur upper edge provides a threshold: eigenvalues above it are retained as candidate common factors, while those at or below it are treated as noise. The matrix is reconstructed by preserving the retained structure and flattening the noise eigenvalues.

The implementation uses a native Jacobi eigendecomposition in MQL5 and applies the cleaned matrix in a basket Expert Advisor. The article describes numerical comparisons with a standard eigensolver and rolling simulations for baskets of four and twelve instruments, reporting improved matrix and weight stability rather than a trading-performance gain. The approach is a practical heuristic: its theoretical assumptions do not hold exactly for market returns, whose volatility and correlations change over time. The example EA also uses simplified sizing and omits transaction-cost and margin-aware modeling, so the denoising step should be treated as risk-input preprocessing rather than a complete portfolio solution.

Key ideas

• Finite return windows can make sample correlation matrices and downstream portfolio weights unstable.
• The Marchenko–Pastur upper edge is used to distinguish candidate signal eigenvalues from sampling noise.
• The method reconstructs the matrix by retaining large eigenvalues and averaging the smaller ones.
• A native Jacobi algorithm makes symmetric-matrix eigendecomposition possible within MQL5.
• The reported evidence concerns matrix and weight stability, while market nonstationarity limits the theoretical threshold’s precision.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.