Coarse graining correlation matrices according to macrostructures: Financial markets as a paradigm

ArXiv ID: 2402.05364 “View on arXiv”

Authors: Unknown

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.

Keywords: Correlation Matrices, Coarse Graining, Market Structure, Statistical Physics, Guhr Matrices, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: 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.

  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"]