Multivariate Distributions in Non-Stationary Complex Systems II: Empirical Results for Correlated Stock Markets

Abstract

Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the non-stationarity typically found in complex systems. Here, we apply these results to the returns measured in correlated stock markets. Only the knowledge of the multivariate return distributions allows for a full-fledged risk assessment. We analyze intraday data of 479 US stocks included in the S&P500 index during the trading year of 2014. We focus particularly on the tails which are algebraic and heavy. The non-stationary fluctuations of the correlations make the tails heavier. With the few-parameter formulae of our Random Matrix Model we can describe and quantify how the empirical distributions change for varying time resolution and in the presence of non-stationarity.

References in corpus (25)

• A Random Matrix Approach to Cross-Correlations in Financial Data
• A New Method to Estimate the Noise in Financial Correlation Matrices
• Non-Stationarity in Financial Time Series and Generic Features
• Impact of the tick-size on financial returns and correlations
• Uncovering the Dynamics of Correlation Structures Relative to the Collective Market Motion
• Identifying long-term precursors of financial market crashes using correlation patterns
• Stability and Hierarchy of Quasi-Stationary States: Financial Markets as an Example
• Cross-response in correlated financial markets: individual stocks
• Average cross-responses in correlated financial market
• Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example
• Compensating asynchrony effects in the calculation of financial correlations
• Credit Risk and the Instability of the Financial System: an Ensemble Approach
• Zooming into market states
• A New Attempt to Identify Long-term Precursors for Endogenous Financial Crises in the Market Correlation Structures
• A Copula Approach on the Dynamics of Statistical Dependencies in the US Stock Market
• Collective behavior in the North Rhine-Westphalia motorway network
• Dependence structure of market states
• Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation
• Constructing Analytically Tractable Ensembles of Non-Stationary Covariances with an Application to Financial Data
• Identifying Dominant Industrial Sectors in Market States of the S&P 500 Financial Data
• Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection
• Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation
• Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations
• Multivariate Distributions in Non-Stationary Complex Systems I: Random Matrix Model and Formulae for Data Analysis
• A New Traders' Game? -- Empirical Analysis of Response Functions in a Historical Perspective