Multivariate distributions in non-stationary complex systems II: Empirical results for correlated stock markets

2024-12-16

Journal of Statistical Mechanics: Theory and Experiment

AI Summary

This paper addresses the challenges of modeling multivariate joint distributions and accurately assessing tail risk in nonstationary complex systems—such as financial markets—where conventional methods struggle with time-varying dependence and heavy-tailed dynamics. We propose a parsimonious stochastic matrix model that jointly captures the evolution of time-varying correlations and heavy-tailed structures. Leveraging intraday return data from 479 S&P 500 constituents in 2014, we pioneer the integration of random matrix theory with nonstationary time series analysis and heavy-tailed statistical inference. Empirical results demonstrate that nonstationarity intensifies algebraic tail behavior. The model characterizes the dynamic evolution of the multivariate density function across multiple time scales using a minimal set of interpretable parameters, faithfully reproducing tail thickening induced by correlation drift. It significantly improves the accuracy of extreme-risk measurement for multi-asset portfolios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

Multivariate distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a random matrix model for 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&P 500 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.

Problem

• Modeling multivariate distributions for correlated stock returns
• Assessing risk with heavy-tailed non-stationary market data
• Quantifying distribution changes due to time resolution and correlations

Innovation

• Random Matrix Model captures multivariate correlation structure
• Model quantifies heavy tails from non-stationary fluctuations
• Few-parameter formulae describe empirical distribution changes