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)"]

Cited References (85)

  1. A new traders’ game? — Empirical analysis of response functions in a historical perspective — → 2503.01629
  2. Multivariate distributions in non-stationary complex systems I: A random matrix model and formulae for data analysis — → 2412.11601
  3. Efficient Multi-Change Point Analysis to Decode Economic Crisis Information from the S&P500 Mean Market Correlation — → 2308.00087
  4. Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation — → 2307.12744
  5. Identifying dominant industrial sectors in market states of the S&P 500 financial data (2022) — link
  6. On financial market correlation structures and diversification benefits across and within equity sectors (2022) — link
  7. New collectivity measures for financial covariances and correlations (2022) — link
  8. Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection (2021) — link
and 77 more
  1. Collective behavior in the North Rhine-Westphalia motorway network (2021) — link
  2. A new attempt to identify long-term precursors for endogenous financial crises in the market correlation structures (2021) — link
  3. Dynamics of the market states in the space of correlation matrices with applications to financial markets (2021) — link
  4. Exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations of covariances or correlations (2020) — link
  5. Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example (2020) — link
  6. Identification of structural multivariate GARCH models (2020) — link
  7. Uncovering the dynamics of correlation structures relative to the collective market motion (2020) — link
  8. Market states: A new understanding (2020) — link
  9. High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019) — link
  10. Econophysics and sociophysics: Their milestones & challenges (2019) — link
  11. Reprint of: Mahalanobis, P.C. (1936) “On the Generalised Distance in Statistics.” (2018) — link
  12. Identifying long-term precursors of financial market crashes using correlation patterns (2018) — link
  13. Hawkes processes and their applications to finance: a review (2018) — link
  14. Extreme Portfolio Loss Correlations in Credit Risk (2017) — link
  15. A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets (2017) — link
  16. Multiplicative Conditional Correlation Models for Realized Covariance Matrices (2016) — link
  17. Concurrent credit portfolio losses (2016) — link
  18. Average cross-responses in correlated financial markets (2016) — link
  19. Cross-response in correlated financial markets: individual stocks (2016) — link
  20. Price response in correlated financial markets: empirical results (2015) — link
  21. Credit Risk: Taking Fluctuating Asset Correlations into Account (2015) — link
  22. Credit risk: taking fluctuating asset correlations into account (2015)
  23. Dependence structure of market states (2015) — link
  24. Constructing analytically tractable ensembles of stochastic covariances with an application to financial data (2015) — link
  25. Stability and hierarchy of quasi-stationary states: financial markets as an example (2015) — link
  26. Dynamics of quasi-stationary systems: Finance as an example (2015) — link
  27. Zooming into market states (2014) — link
  28. Modelling stochastic correlation (2014) — link
  29. Credit risk and the instability of the financial system: An ensemble approach (2013) — link
  30. PORTFOLIO RETURN DISTRIBUTIONS: SAMPLE STATISTICS WITH STOCHASTIC CORRELATIONS (2013) — link
  31. Non-stationarity in financial time series: Generic features and tail behavior (2013) — link
  32. The VIX, the Variance Premium and Stock Market Volatility (2013) — link
  33. Dynamic Conditional Correlation: On Properties and Estimation (2013) — link
  34. Identifying States of a Financial Market (2012) — link
  35. A copula approach on the dynamics of statistical dependencies in the US stock market (2011) — link
  36. Statistical causes for the Epps effect in microstructure noise (2010) — link
  37. The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility (2010) — link
  38. Impact of the tick-size on financial returns and correlations (2010) — link
  39. Power mapping with dynamical adjustment for improved portfolio optimization (2010) — link
  40. Compensating asynchrony effects in the calculation of financial correlations (2009) — link
  41. X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling (2009) — link
  42. A well-conditioned estimator for large-dimensional covariance matrices (2004) — link
  43. What really causes large price changes? (2003) — link
  44. The Long Memory of the Efficient Market (2003) — link
  45. Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes (2003) — link
  46. A theory of power-law distributions in financial market fluctuations (2003) — link
  47. A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model With Time-Varying Correlations (2002) — link
  48. Dynamic Conditional Correlation (2002) — link
  49. A New Method to Estimate the Noise in Financial Correlation Matrices (2002) — link
  50. Quantifying and interpreting collective behavior in financial markets. (2001) — link
  51. Random matrix approach to cross correlations in financial data. (2001) — link
  52. An Introduction to Copulas (2000) — link
  53. An Introduction to Econophysics: Correlations and Complexity in Finance (1999)
  54. Scaling of the distribution of price fluctuations of individual companies. (1999) — link
  55. Scaling of the distribution of fluctuations of financial market indices. (1999) — link
  56. Noise Dressing of Financial Correlation Matrices (1998) — link
  57. Inverse cubic law for the distribution of stock price variations (1998) — link
  58. Finance (1991) — link
  59. Why Does Stock Market Volatility Change Over Time (1988) — link
  60. Comovements in Stock Prices in the Very Short Run (1979) — link
  61. DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES (1967) — link
  62. Global industry classification sector (GICS) (2023)
  63. COVID-19 and March 2020 Stock Market Crash. Evidence from S&P1500 (2020) — link
  64. Data Reduction And Error Analysis For The Physical Sciences (2016)
  65. Multi-Asset Correlation Dynamics with Application to Trading (2015)
  66. New York stock exchange, Daily TAQ (Trade and Quote) (2014)
  67. Standard & Poor’s 500 stock data (2014)
  68. Pricing Foreign Equity Options with Stochastic Correlation and Volatility (2009)
  69. CHAPTER 2 – How Markets Slowly Digest Changes in Supply and Demand (2009) — link
  70. Modelling correlation as a stochastic process (2006)
  71. Asymmetric Volatility and Risk in Equity Markets (1997) — link
  72. Random variables, joint distribution functions, and copulas (1973)
  73. The Variation of Certain Speculative Prices (1963) — link
  74. Fonctions de repartition a n dimensions et leurs marges (1959)
  75. References
  76. S&P Dow
  77. MSCI, S

4 of 85 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.