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

TL;DR

This paper introduces a novel application of the Helmholtz-Hodge-Kodaira decomposition to financial networks, revealing hierarchical causality structures and key crisis drivers during COVID-19 using Granger causality analysis.

Contribution

It applies the Helmholtz-Hodge-Kodaira decomposition to financial causality networks, uncovering hierarchical structures and identifying crisis-driving sectors during COVID-19.

Findings

Precious metals and pharmaceuticals are causal drivers during COVID-19

Crisis periods show increased network connectivity

Decomposition reveals hierarchical causality flow

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.