Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes

TL;DR

This paper introduces a random-matrix model based on covariance matrices of coupled Ornstein-Uhlenbeck processes, revealing localization transitions and correlations in financial time-series.

Contribution

It provides a novel random-matrix ensemble model for analyzing heterogeneous financial data and explains localization phenomena in eigenvectors related to market volatility.

Findings

Spectral properties align with stylized facts of financial markets.

Evidence of localization transition in eigenvectors.

Inverted-bell effect observed in correlation between localization and volatility.

Abstract

We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the presented model formulas are given for the analysis of heterogeneous time-series. Furthermore evidence for a localization transition in eigenvectors related to small and large eigenvalues in cross-correlations analysis of this model is found and a simple explanation of localization phenomena in financial time-series is provided. Finally we identify both in our model and in real financial data an inverted-bell effect in correlation between localized components and their local temperature: high and low temperature/volatility components are the most localized ones.