Universal and non-universal properties of cross-correlations in financial time series

Abstract

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum--a situation reminiscent of results in localization theory.

14 pages, 3 figures, Revtex

References in corpus (7)

• Noise Dressing of Financial Correlation Matrices
• Inverse Cubic Law for the Probability Distribution of Stock Price Variations
• A Langevin Approach to Stock Market Fluctuations and Crashes
• Universal features in the growth dynamics of complex organizations
• Ivory Tower Universities and Competitive Business Firms
• A generalized spin model of financial markets
• Rational Decisions, Random Matrices and Spin Glasses

Cited by in corpus (296)

• Statistical physics of human cooperation
• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• A Random Matrix Approach to Cross-Correlations in Financial Data
• Dynamics of market correlations: Taxonomy and portfolio analysis
• Scaling of the distribution of price fluctuations of individual companies
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Topology of correlation based minimal spanning trees in real and model markets
• Induced measures in the space of mixed quantum states
• Networks of equities in financial markets
• Multifractal analysis of financial markets
• Correlation, hierarchies, and networks in financial markets
• Correlation of financial markets in times of crisis
• Weighted network modules
• Application of Random Matrix Theory to Biological Networks
• Multiscale characteristics of the emerging global cryptocurrency market
• Spectra and eigenvectors of scale-free networks
• Evolution of worldwide stock markets, correlation structure and correlation based graphs
• Correlation based networks of equity returns sampled at different time horizons
• Random Matrix Theory Analysis of Cross Correlations in Financial Markets
• Volatility clustering and scaling for financial time series due to attractor bubbling
• Taxonomy of Stock Market Indices
• Collective behavior of stock price movements in an emerging market
• Correlation, Network and Multifractal Analysis of Global Financial Indices
• Mutual Information Rate-Based Networks in Financial Markets
• Worldwide spreading of economic crisis
• Systematic analysis of group identification in stock markets
• Spanning Trees and bootstrap reliability estimation in correlation based networks
• Community detection for correlation matrices
• Topology of Foreign Exchange Markets using Hierarchical Structure Methods
• Spectra of Sparse Random Matrices
• Quantifying and Modeling Long-Range Cross-Correlations in Multiple Time Series with Applications to World Stock Indices
• Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model
• Cross-correlation in financial dynamics
• Dynamics of competition between collectivity and noise in the stock market
• Temporal Evolution of Financial Market Correlations
• Characteristics of the Korean stock market correlations
• Sector analysis for a FTSE portfolio of stocks
• Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices
• Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
• Correlations, Risk and Crisis: From Physiology to Finance
• Scale-free Network in Financial Correlations
• Systemic risk and spatiotemporal dynamics of the US housing market
• A model for correlations in stock markets
• Statistics of Atmospheric Correlations
• Noisy Covariance Matrices and Portfolio Optimization II
• A New Methodology of Spatial Crosscorrelation Analysis
• Levels of complexity in financial markets
• Variety and Volatility in Financial Markets
• Estimated Correlation Matrices and Portfolio Optimization
• Universality in Complex Networks: Random Matrix Analysis
• Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode
• Random matrix analysis of complex networks
• Structure of local interactions in complex financial dynamics
• A New Method to Estimate the Noise in Financial Correlation Matrices
• Towards identifying the world stock market cross-correlations: DAX versus Dow Jones
• An analysis of Cross-correlations in South African Market data
• Increasing market efficiency: Evolution of cross-correlations of stock returns
• Cross-Correlation Dynamics in Financial Time Series
• Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws
• Data clustering and noise undressing for correlation matrices
• Kullback-Leibler distance as a measure of the information filtered from multivariate data
• The structural role of weak and strong links in a financial market network
• Evolution of correlation structure of industrial indices of US equity markets
• The bulk of the stock market correlation matrix is not pure noise
• Specialization of strategies and herding behavior of trading firms in a financial market
• Evaluating the RiskMetrics Methodology in Measuring Volatility and Value-at-Risk in Financial Markets
• Random Matrix Theory and Fund of Funds Portfolio Optimisation
• Spectral Moments of Correlated Wishart Matrices
• Identifying phase synchronization clusters in spatially extended dynamical systems
• Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices
• Non-Stationarity in Financial Time Series and Generic Features
• Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
• Record Statistics for Multiple Random Walks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Dynamic evolution of cross-correlations in the Chinese stock market
• Hierarchically nested factor model from multivariate data
• Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia
• Large Scale Cross-Correlations in Internet Traffic
• Signal and Noise in Financial Correlation Matrices
• Stochastic Cellular Automata Model for Stock Market Dynamics
• Anti-correlation and subsector structure in financial systems
• Trading strategies in the Italian interbank market
• Adaptive financial networks with static and dynamic thresholds
• Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
• Competition of noise and collectivity in global cryptocurrency trading: route to a self-contained market
• Subsystem dynamics under random Hamiltonian evolution
• Portfolio Optimization and the Random Magnet Problem
• Hausdorff clustering of financial time series
• Carbon-dioxide emissions trading and hierarchical structure in worldwide finance and commodities markets
• Spectral and network methods in the analysis of correlation matrices of stock returns
• Random matrix analysis of localization properties of Gene co-expression network
• Correlation structure and principal components in global crude oil market
• Measures of globalization based on cross-correlations of world financial indices
• Quantitative law describing market dynamics before and after interest-rate change
• Topological structures in the equities market network
• Statistical Properties of Cross-Correlation in the Korean Stock Market
• Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations
• Random Matrix Theory and Cross-correlations in Global Financial Indices and Local Stock Market Indices
• Identifying long-term precursors of financial market crashes using correlation patterns
• Scale free effects in world currency exchange network
• Market correlation structure changes around the Great Crash
• Time scales involved in market emergence
• Agent-based model with multi-level herding for complex financial systems
• Quantifying dynamics of the financial correlations
• Cross-correlation markers in stochastic dynamics of complex systems
• Crashes, Recoveries, and `Core-shifts' in a Model of Evolving Networks
• Probing many-body localization by excited-state VQE
• The q-dependent detrended cross-correlation analysis of stock market
• Dynamic instability in a phenomenological model of correlated assets
• Configuration model for correlation matrices preserving the node strength
• Random matrix analysis of network Laplacians
• Characterizing Multi-Scale Self-Similar Behavior and Non-Statistical Properties of Financial Time Series
• Dynamic scaling approach to study time series fluctuations
• World currency exchange rate cross-correlations
• Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks
• Random Matrix Spectra as a Time Series
• Persistence Probabilities of the German DAX and Shanghai Index
• Modelling gap-size distribution of parked cars using random-matrix theory
• What is mature and what is still emerging in the cryptocurrency market?
• Large Pseudo-Counts and $L_2$-Norm Penalties Are Necessary for the Mean-Field Inference of Ising and Potts Models
• Risk Minimization through Portfolio Replication
• On return-volatility correlation in financial dynamics
• Spectral transitions in networks
• How much random a random network is : a random matrix analysis
• Regularizing Portfolio Optimization
• On the concentration of large deviations for fat tailed distributions, with application to financial data
• Spectral Density of Sparse Sample Covariance Matrices
• The fine structure of spectral properties for random correlation matrices: an application to financial markets
• Spectral analysis of deformed random networks
• Correlations and Flow of Information between The New York Times and Stock Markets
• Influence network in Chinese stock market
• Credit risk - A structural model with jumps and correlations
• Club Convergence of House Prices: Evidence from China's Ten Key Cities
• Universal Correlations and Power-Law Tails in Financial Covariance Matrices
• Efficient construction of threshold networks of stock markets
• Cross correlations of the American baby names
• Introduction to correlation networks: Interdisciplinary approaches beyond thresholding
• The effect of a market factor on information flow between stocks using minimal spanning tree
• Forecasting the underlying potential governing the time series of a dynamical system
• A Random Matrix Approach to VARMA Processes
• Quantifying randomness in protein-protein interaction networks of different species: A random matrix approach
• Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles
• Determining the number of factors in a forecast model by a random matrix test: cryptocurrencies
• A Study of Correlations in the Stock Market
• Symmetry deduction from spectral fluctuations in complex quantum systems
• On the non-stationarity of financial time series: impact on optimal portfolio selection
• Scaling in the eigenvalue fluctuations of the empirical correlation matrices
• Asymmetric correlation matrices: an analysis of financial data
• Replica approach to mean-variance portfolio optimization
• Family of solvable generalized random-matrix ensembles with unitary symmetry
• Multiscaled Cross-Correlation Dynamics in Financial Time-Series
• Hierarchical structure of the European countries based on debts as a percentage of GDP during the 2000-2011 period
• Lead-lag Relationships in Foreign Exchange Markets
• Zooming into market states
• Spectral analysis of finite-time correlation matrices near equilibrium phase transitions
• Cross-correlation asymmetries and causal relationships between stock and market risk
• Spectral analysis of Gene co-expression network of Zebrafish
• Random Matrix Theory and the Failure of Macroeconomic Forecasts
• Time vs. Ensemble Averages for Nonstationary Time Series
• State and group dynamics of world stock market by principal component analysis
• Evidence of Increment of Efficiency of the Mexican Stock Market Through the Analysis of its Variations
• Constructing networks by filtering correlation matrices: A null model approach
• Towards a common thread in Complexity: an accuracy-based approach
• Emerging spectra of singular correlation matrices under small power-map deformations
• Long-Time Fluctuations in a Dynamical Model of Stock Market Indices
• Non-Hermitean Wishart random matrices (I)
• Identifying Complexity by Means of Matrices
• Extreme-value statistics of networks with inhibitory and excitatory couplings
• Spectral methods and cluster structure in correlation-based networks
• Universal Spectral Correlations in Orthogonal-Unitary and Symplectic-Unitary Crossover Ensembles of Random Matrices
• Spectral Domain of Large Nonsymmetric Correlated Wishart Matrices
• Alternation of different fluctuation regimes in the stock market dynamics
• Random matrix approach to the dynamics of stock inventory variations
• Emergence of frustration signals systemic risk
• Hausdorff clustering
• Random matrix analysis of deep neural network weight matrices
• Effects of time dependency and efficiency on information flow in financial markets
• The Convergence of European Business Cycles 1978-2000
• Multiple Time Series Ising Model for Financial Market Simulations
• Financial time-series analysis: A brief overview
• Nature of order from random two-body interactions
• Random matrix approach to multivariate categorical data analysis
• Memory effect and multifractality of cross-correlations in financial markets
• Spatial and temporal structures of four financial markets in Greater China
• Approaching multifractal complexity in decentralized cryptocurrency trading
• Spectral density of a Wishart model for nonsymmetric Correlation Matrices
• Spectrum, Intensity and Coherence in Weighted Networks of a Financial Market
• Random, but not so much: A parameterization for the returns and correlation matrix of financial time series
• A Structural Model for Fluctuations in Financial Markets
• New Collectivity Measures for Financial Covariances and Correlations
• Maximum Entropy approach to multivariate time series randomization
• Quantifying the status of economies in international crop trade networks: An correlation structure analysis of various node-ranking metrics
• Distribution of the Smallest Eigenvalue in Complex and Real Correlated Wishart Ensembles
• Analysis of risk propagation using the world trade network
• Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation
• Non-Stationary Covariance Matrices And Noise
• Projecting XRP price burst by correlation tensor spectra of transaction networks
• Eigenfunction statistics of Laguerre Brownian ensemble
• Effect of changing data size on eigenvalues in the Korean and Japanese stock markets
• Correlation Patterns in Foreign Exchange Markets
• Dependence structure of market states
• Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
• Decomposing the stock market intraday dynamics
• From human mobility to renewable energies: Big data analysis to approach worldwide multiscale phenomena
• Correlations and clustering in the trading of members of the London Stock Exchange
• How volatilities nonlocal in time affect the price dynamics in complex financial systems
• Correlations versus noise in the NFT market
• Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation
• Saturation of number variance in embedded random matrix ensembles
• Constructing Analytically Tractable Ensembles of Non-Stationary Covariances with an Application to Financial Data
• Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
• Localization in random bipartite graphs: numerical and empirical study
• Correlation Matrix Spectra: A Tool for Detecting Non-apparent Correlations?
• Eigenvector localization as a tool to study small communities in online social networks
• Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE
• Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market
• Finite-Range Coulomb Gas Models I: Some Analytical Results
• Free Random Levy Variables and Financial Probabilities
• Plant responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience
• Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models
• Spectra of Empirical Auto-Covariance Matrices
• Spacing ratio statistics of multiplex directed networks
• Analysis of delay correlation matrices
• Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes
• Identifying Dominant Industrial Sectors in Market States of the S&P 500 Financial Data
• Optimal design of experiments by combining coarse and fine measurements
• Note on log-periodic description of 2008 financial crash
• A microscopic model of triangular arbitrage
• Complex Correlation Approach for High Frequency Financial Data
• Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness
• Universal dynamic scaling in chemical reactions at and away from equilibrium
• Universal Statistics of Competition in Democratic Elections
• Emerging interdependence between stock values during financial crashes
• Predicting trend reversals using market instantaneous state
• Nonextensive triplets in stock market indices
• Eigenvalue and Eigenvector Statistics in Time Series Analysis
• Filtering of complex systems using overlapping tree networks
• Exact finite-size scaling for the random-matrix representation of bond percolation on square lattice
• Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
• Spectrum concentration in deep residual learning: a free probability approach
• Global correlation matrix spectra of the surfacetemperature of the Oceans from Random MatrixTheory to Poisson fluctuations
• Random matrix approach for primal-dual portfolio optimization problems
• Universal Fluctuations of AEX index
• Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation
• Spectral density of the non-central correlated Wishart ensembles
• Coherence and incoherence collective behavior in financial market
• Finite size effects. The averaged eigenvalue density of Wigner random sign real symmetric matrices
• Accounting for risk of non linear portfolios: a novel Fourier approach
• Unveiling the directional network behind the financial statements data using volatility constraint correlation
• Eigenvector localization in hypergraphs: pair-wise vs higher-order links
• Matrix H-theory approach to stock market fluctuations
• Fractal behind smart shopping
• A 2D Levy-flight model for the complex dynamics of real-life financial markets
• Dynamic structure of stock communities: A comparative study between stock returns and turnover rates
• Causality and Correlations between BSE and NYSE indexes: A Janus Faced Relationship
• Geography and distance effect on financial dynamics in the Chinese stock market
• Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data
• Universality and scaling in human and social systems
• Cluster formation and evolution in networks of financial market indices
• Interaction-correlated random matrices
• Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations
• Boundary between noise and information applied to filtering neural network weight matrices
• Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
• The ETS challenges: a machine learning approach to the evaluation of simulated financial time series for improving generation processes
• Random matrix approach in search for weak signals immersed in background noise
• Counting Multiple Solutions in Glassy Random Matrix Models
• Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime
• Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles
• Signal from noise retrieval from one and two-point Green's function - comparison
• Random selection of factors preserves the correlation structure in a linear factor model to a high degree
• Large-Scale Simulation of Multi-Asset Ising Financial Markets
• Assessing the Predictability of Social and Economic Time-Series Data: the example of crime in the UK
• Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error
• From Space and Time to a Deeper Reality as a Possible Way to Solve Global Problems
• The Effects of Market Properties on Portfolio Diversification in the Korean and Japanese Stock Markets
• Scaling analysis of stationary probability distributions of random walks on one-dimensional lattices with aperiodic disorder
• Separating Putative Pathogens from Background Contamination with Principal Orthogonal Decomposition: Evidence for Leptospira in the Ugandan Neonatal Septisome
• Patterns for the waiting time in the context of discrete-time stochastic processes
• Co-clustering of Fuzzy Lagged Data
• Matrix Moments in a Real, Doubly Correlated Algebraic Generalization of the Wishart Model
• Removing noise from correlations in multivariate stock price data
• Dynamic analysis of influential stocks based on conserved networks
• Worldwide bilateral geopolitical interactions network inferred from national disciplinary profiles
• Characterizing price index behavior through fluctuation dynamics
• The Volatility in a Multi-share Financial Market Model
• Inferring financial stock returns correlation from complex network analysis
• On the extremal spectral properties of random graphs
• Signal inference in financial stock return correlations through phase-ordering kinetics in the quenched regime
• Random Matrix Time Series
• Plunges in the Bombay stock exchange: Characteristics and indicators
• Evolutionary dynamics in financial markets with heterogeneities in strategies and risk tolerance
• Generic Features in the Spectral Decomposition of Correlation Matrices
• Normal mode analysis of disordered random-matrix ensembles
• Assessment of Spatial-variant Noise Level in Real-time Dynamic MR Images - a Random Matrix Approach
• Random Matrix Application to Correlations Among Volatility of Assets
• Optimal trading strategies - a time series approach