Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes

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.

arXiv comment6 pages, 4 figures

References in corpus (17)

• Noise Dressing of Financial Correlation Matrices
• Universal and non-universal properties of cross-correlations in financial time series
• A Random Matrix Approach to Cross-Correlations in Financial Data
• The statistical properties of the volatility of price fluctuations
• Analysis of data sets of stochastic systems
• Volatility distribution in the S&P500 Stock Index
• Random Matrix Theory Analysis of Cross Correlations in Financial Markets
• Collective behavior of stock price movements in an emerging market
• Spectral Statistics: From Disordered to Chaotic Systems
• Volatility in Financial Markets: Stochastic Models and Empirical Results
• Are random trading strategies more successful than technical ones?
• The bulk of the stock market correlation matrix is not pure noise
• Spectral Moments of Correlated Wishart Matrices
• Eigenvalue Density of Correlated Complex Random Wishart Matrices
• Signal and Noise in Financial Correlation Matrices
• Spectral properties of empirical covariance matrices for data with power-law tails
• Universal Correlations and Power-Law Tails in Financial Covariance Matrices

Cited by in corpus (5)

• netrd: A library for network reconstruction and graph distances
• Emergence of frustration signals systemic risk
• Eigenvalue and Eigenvector Statistics in Time Series Analysis
• Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
• Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability