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.
Keywords
Cite
@article{arxiv.2412.11602,
title = {Multivariate Distributions in Non-Stationary Complex Systems II: Empirical Results for Correlated Stock Markets},
author = {Anton J. Heckens and Efstratios Manolakis and Cedric Schuhmann and Thomas Guhr},
journal= {arXiv preprint arXiv:2412.11602},
year = {2025}
}