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arXiv · 2412.11602

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

Anton J. Heckens·Efstratios Manolakis·Cedric Schuhmann·Thomas Guhr
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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.

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Anton J. Heckens, Efstratios Manolakis, Cedric Schuhmann, Thomas Guhr. 2024-12-16. Multivariate Distributions in Non-Stationary Complex Systems II: Empirical Results for Correlated Stock Markets. https://doi.org/10.1088/1742-5468%2Fade5f9

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