Paper: arXiv 2412.11602

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper uses advanced Random Matrix Theory and multivariate distributions with heavy algebraic tails, demonstrating high mathematical density. It also shows strong empirical rigor by analyzing high-frequency intraday data from 479 stocks, implementing specific data cleaning and normalization procedures, and validating model predictions against observed non-stationarity effects.

Research Flowchart

  flowchart TD
  A["Research Goal: Quantify impact of non-stationarity<br>on multivariate stock return distributions"] --> B["Methodology: Random Matrix Model<br>for Multivariate PDFs"]
  B --> C["Data Input: Intraday returns<br>479 US stocks, S&P500, 2014"]
  C --> D["Computational Process: Fit model &<br>analyze tails across varying time resolutions"]
  D --> E["Key Finding: Correlations are non-stationary"]
  E --> F["Outcome: Non-stationarity increases<br>tail heaviness (Risk Assessment)"]