Causal Hierarchy in the Financial Market Network – Uncovered by the Helmholtz-Hodge-Kodaira Decomposition

ArXiv ID: 2408.12839 “View on arXiv”

Authors: Unknown

Abstract

Granger causality can uncover the cause and effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into a rotational and gradient component which reveals the hierarchy of Granger causality flow. Using Kenneth French’s business sector return time series, it is revealed that during the Covid crisis, precious metals and pharmaceutical products are causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during crisis which means that the research presented here can be especially useful to better understand crises in the market by revealing the dominant drivers of the crisis dynamics.

Keywords: Granger Causality, Helmholtz-Hodge-Kodaira Decomposition, Financial Networks, Time Series Analysis, Causality Flow, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like Granger causality, Helmholtz-Hodge-Kodaira decomposition, and PCA, with dense derivations, but is grounded in a specific financial dataset (Kenneth French’s 49 sectors) with detailed estimation procedures and empirical results during the Covid crisis.

  flowchart TD
    Start["Research Goal: Analyze the hierarchical structure of causality in financial markets during the Covid crisis"] --> InputData["Input: Kenneth French business sector return time series"]
    InputData --> GC["Methodology: Construct Granger Causality Network"]
    GC --> Decomp["Computational Process: Helmholtz-Hodge-Kodaira Decomposition"]
    Decomp --> Comp1["Gradient Component (Potential Flow)"]
    Decomp --> Comp2["Rotational Component (Cyclic Flow)"]
    Comp1 --> Hierarchy["Output: Causal Hierarchy Extraction"]
    Comp2 --> Hierarchy
    Hierarchy --> Findings["Key Findings: Precious metals & pharmaceuticals as causal drivers; High network connectivity during crisis"]