Universal Correlations and Power-Law Tails in Financial Covariance Matrices

TL;DR

This paper investigates the universal properties and deviations in the eigenvalue spectra of financial covariance matrices, revealing robustness in local eigenvalue statistics and power-law correlations in global spectral density.

Contribution

It introduces a chopping procedure to generate statistical ensembles from single financial datasets and compares spectral properties to random matrix models, highlighting universal and non-universal features.

Findings

Local eigenvalue statistics match universal distributions like Tracy-Widom and Wigner surmise.

Global spectral density deviates from standard random matrix predictions.

Power-law decay correlations are observed in the spectral data.

Abstract

Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.