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

TL;DR

This paper applies a Random Matrix Model to analyze non-stationary, correlated stock market returns, revealing how heavy tails and correlation fluctuations impact risk assessment in financial systems.

Contribution

It extends previous models by empirically demonstrating how non-stationarity affects multivariate return distributions in stock markets.

Findings

Heavy tails in return distributions are amplified by non-stationary correlations.

The Random Matrix Model accurately describes empirical distribution changes over different time resolutions.

Non-stationarity significantly influences risk assessment through tail behavior.

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.