Eigenvalue distribution of empirical correlation matrices for multiscale complex systems and application to financial...

Area of Science:

• Quantitative Finance
• Statistical Physics
• Time Series Analysis

Background:

• Traditional analysis of financial markets often treats them as 'noise-dressed', overlooking underlying structures.
• Multivariate time series data in finance present complex correlation patterns that are challenging to model accurately.

Purpose of the Study:

• To introduce a novel method for describing eigenvalue distributions of correlation matrices from multidimensional financial time series.
• To improve the characterization of empirical correlation matrices by incorporating market complexity and informational cascades.

Main Methods:

• Development of matrix H theory to analyze eigenvalue spectra.
• Modeling informational cascades as hierarchical structures, drawing parallels with Kolmogorov's turbulence theory.
• Extension of the Marchenko-Pastur distribution to include characteristic scales.

Main Results:

• The new method improves the description of eigenvalue spectra for empirical correlation matrices.
• The approach captures a larger fraction of data variance by accounting for distinct characteristic scales.
• The findings challenge the traditional view of financial markets as purely noise-driven.

Conclusions:

• The effectiveness of the method is attributed to the increasing complexity and characteristic scales in modern financial markets.
• The study supports the turbulent market hypothesis as a source of market noise.
• A practical framework is provided for noise reduction in correlation matrices, enhancing the inference of asset correlations.