Empirics versus RMT in financial cross-correlations

TL;DR

This paper investigates the relationship between financial cross-correlations and Random Matrix Theory, revealing complex, nonlinear market structures that challenge traditional decompositions into market and sector components.

Contribution

It provides a comprehensive analysis of correlation matrix characteristics, demonstrating that market dynamics are more intricate than standard models suggest.

Findings

Market dynamics are not simply decomposable into 'market', 'sectors', and random bulk.

Longer time series reveal hierarchical, nonlinear market organization.

Relevant market information is encoded in individual constituents.

Abstract

In order to pursue the issue of the relation between the financial cross-correlations and the conventional Random Matrix Theory we analyse several characteristics of the stock market correlation matrices like the distribution of eigenvalues, the cross-correlations among signs of the returns, the volatility cross-correlations, and the multifractal characteristics of the principal values. The results indicate that the stock market dynamics is not simply decomposable into 'market', 'sectors', and the Wishart random bulk. This clearly is seen when the time series used to construct the correlation matrices are sufficiently long and thus the measurement noise suppressed. Instead, a hierarchically convoluted and highly nonlinear organization of the market emerges and indicates that the relevant information about the whole market is encoded already in its constituents.