Zooming into market states

Abstract

We analyze the daily stock data of the Nasdaq Composite index in the 22-year period 1992-2013 and identify market states as clusters of correlation matrices with similar correlation structures. We investigate the stability of the correlation structure of each state by estimating the statistical fluctuations of correlations due to their non-stationarity. Our study is based on a random matrix approach recently introduced to model the non-stationarity of correlations by an ensemble of random matrices. This approach reduces the complexity of the correlated market to a single parameter which characterizes the fluctuations of the correlations and can be determined directly from the empirical return distributions. This parameter provides an insight into the stability of the correlation structure of each market state as well as into the correlation structure dynamics in the whole observation period. The analysis reveals an intriguing relationship between average correlation and correlation fluctuations. The strongest fluctuations occur during periods of high average correlation which is the case particularly in times of crisis.

arXiv comment13 pages, 9 figures

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• Spatial Correlation Analysis of Traffic Flow on Parallel Motorways in Germany
• New Collectivity Measures for Financial Covariances and Correlations
• Compounding approach for univariate time series with non-stationary variances
• Transitions between quasi-stationary states in traffic systems: Cologne orbital motorways as an example
• Multivariate Distributions in Non-Stationary Complex Systems I: Random Matrix Model and Formulae for Data Analysis
• Ordinal Synchronization and Typical States in High-Frequency Digital Markets
• Multivariate Distributions in Non-Stationary Complex Systems II: Empirical Results for Correlated Stock Markets