Paper: arXiv 2402.05364

Abstract

We analyze correlation structures in financial markets by coarse graining the Pearson correlation matrices according to market sectors to obtain Guhr matrices using Guhr’s correlation method according to Ref. [“P. Rinn {"\it et. al.”}, Europhysics Letters 110, 68003 (2015)"]. We compare the results for the evolution of market states and the corresponding transition matrices with those obtained using Pearson correlation matrices. The behavior of market states is found to be similar for both the coarse grained and Pearson matrices. However, the number of relevant variables is reduced by orders of magnitude.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced mathematical techniques like Guhr’s correlation method and dimensionality reduction, resulting in a high math score; however, it focuses on theoretical analysis of market states without providing specific trading strategies, performance metrics, or code, leading to a lower empirical rigor score.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Analyze correlation structures in financial markets<br>by coarse graining Pearson matrices"] --> B{"Data Input<br>Financial Market Equity Returns"}
  B --> C["Methodology Step 1<br>Compute Pearson Correlation Matrix"]
  B --> D["Methodology Step 2<br>Apply Macrostructure Coarse Graining<br>using Market Sectors"]
  C --> E["Computational Process<br>Guhr's Correlation Method"]
  D --> E
  E --> F["Outcome 1<br>Coarse Grained Guhr Matrices"]
  F --> G["Comparative Analysis<br>Evolution of Market States &<br>Transition Matrices"]
  G --> H["Key Findings<br>Similar market state behavior<br>Reduced variables by orders of magnitude"]

Cited References (43)

  1. Identifying Long-Term Precursors of Financial Market Crashes Using Correlation Patterns (2018) — link
  2. Identifying States of a Financial Market (2012) — link
  3. Complex Market Dynamics in the Light of Random Matrix Theory (2019) — link
  4. Dynamics of market states and risk assessment (2024) — link
  5. An Introduction to Econophysics: Correlations and Complexity in Finance (2000)
  6. Noise Dressing of Financial Correlation Matrices (1999) — link
  7. A new attempt to identify long-term precursors for endogenous financial crises in the market correlation structures (2022) — link
  8. New collectivity measures for financial covariances and correlations (2022) — link
and 35 more
  1. PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE (2004) — link
  2. Correlations beyond the trend: A financial market analysis (in prep. (2023))
  3. The Advanced Theory of Statistics, Volume 2: Inference and Relationship (1973)
  4. Market state dynamics in correlation matrix space (in press 2023)
  5. A new method to estimate the noise in financial correlation matrices (2003) — link
  6. Local normalization: Uncovering correlations in non-stationary financial time series (2010) — link
  7. Emerging spectra of singular correlation matrices under small power-map deformations (2013) — link
  8. Modern Multidimensional Scaling: Theory and Applications (2005) — link
  9. Supplemental Material: COVID anomaly in the correlation analysis of S&P 500 market states (2023)
  10. Economic state classification and portfolio optimisation with application to stagflationary environments (2022) — link
  11. Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example (2020) — link
  12. A network-based method for detecting critical events of correlation dynamics in financial markets (2020) — link
  13. Uncovering the dynamics of correlation structures relative to the collective market motion (2020) — link
  14. Structural model for fluctuations in financial markets (2018) — link
  15. Characterisation of survivability resilience with dynamic stock interdependence in financial networks (2018) — link
  16. Immediate causality network of stock markets (2018) — link
  17. A new perspective on Financial Market States: Sectorial Analysis (in prep. (2023))
  18. Coarse graining correlation matrices with applications in financial markets (in prep. (2023))
  19. WHO Director-General’s opening remarks at the media briefing on COVID-19—11 March 2020 (March 2020)
  20. COVID anomaly in the correlation analysis of S&P 500 market states (2024) — link
  21. 2023 Yahoo finance database (accessed on 11 August, 2023 for S&P 500)
  22. Dynamics of quasi-stationary systems: Finance as an example (2015) — link
  23. Theory of financial risk and derivative pricing: from statistical physics to risk management (2003)
  24. Multivariate observations (2009)
  25. K-means clustering tutorial (2006)
  26. Data clustering: 50 years beyond K-means (2010)
  27. THE ECONOMETRICS OF FINANCIAL MARKETS (1998)
  28. Taxonomy of stock market indices (2000)
  29. High-frequency cross-correlation in a set of stocks (2001)
  30. Hierarchical structure in financial markets (1999)
  31. Degree stability of a minimum spanning tree of price return and volatility (2003)
  32. Cluster analysis for portfolio optimization. Journal of Economic Dynamics & Control (2008)
  33. Correlation, hierarchies, and networks in financial markets (2010)
  34. Quantum channels and memory effects (2014) — link
  35. Sub-Narrow Band Sleep Stage Analysis - Eigenvalues and Eigenvectors of the Multi-Band Cross-Correlation Matrix - (submitted to Physica A (2024))

0 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.