Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data

TL;DR

This paper presents a novel matrix H theory to analyze eigenvalue distributions of correlation matrices in multiscale complex systems, especially financial markets, improving noise filtering and revealing underlying structures.

Contribution

It extends the Marchenko-Pastur distribution to include multiple characteristic scales, offering a new framework for understanding complex correlations in financial data.

Findings

Enhanced eigenvalue spectrum description for financial correlation matrices

Identification of new characteristic scales in market data

Support for turbulence-based market noise hypothesis

Abstract

We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation matrices in multivariate financial data by considering an informational cascade modeled as a hierarchical structure akin to the Kolmogorov statistical theory of turbulence. Our approach extends the Marchenko-Pastur distribution to account for distinct characteristic scales, capturing a larger fraction of data variance, and challenging the traditional view of noise-dressed financial markets. We conjecture that the effectiveness of our method stems from the increased complexity in financial markets, reflected by new characteristic scales and the growth of computational trading. These findings not only support the turbulent market hypothesis as a source of noise but also provide a practical framework for noise reduction in empirical correlation matrices, enhancing the inference of true market correlations between assets.