Paper: arXiv 2502.14431

Abstract

The paper presents a comprehensive causality analysis of the US stock and commodity markets during the COVID-19 crash. The dynamics of different sectors are also compared. We use Topological Data Analysis (TDA) on multidimensional time-series to identify crashes in stock and commodity markets. The Wasserstein Distance WD shows distinct spikes signaling the crash for both stock and commodity markets. We then compare the persistence diagrams of stock and commodity markets using the WD metric. A significant spike in the $WD$ between stock and commodity markets is observed during the crisis, suggesting significant topological differences between the markets. Similar spikes are observed between the sectors of the US market as well. Spikes obtained may be due to either a difference in the magnitude of crashes in the two markets (or sectors), or from the temporal lag between the two markets suggesting information flow. We study the Granger-causality between stock and commodity markets and also between different sectors. The results show a bidirectional Granger-causality between commodity and stock during the crash period, demonstrating the greater interdependence of financial markets during the crash. However, the overall analysis shows that the causal direction is from stock to commodity. A pairwise Granger-causal analysis between US sectors is also conducted. There is a significant increase in the interdependence between the sectors during the crash period. TDA combined with Granger-causality effectively analyzes the interdependence and sensitivity of different markets and sectors.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced mathematics including Topological Data Analysis (TDA), persistent homology, and Vietoris–Rips complexes, which require significant theoretical understanding. However, the empirical component relies on a specific historical event (COVID-19 crash) with no mention of backtesting, live implementation, or robust out-of-sample validation, making it more of a theoretical exercise.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Analyze COVID-19 crash causality<br>in Stock & Commodity Markets"] --> B["Data: Multidimensional Time-Series<br>US Stock & Commodity Markets"]
  B --> C{"Key Methodology"}
  C --> D["TDA: Wasserstein Distance<br>Identify Crash Spikes"]
  C --> E["Granger Causality<br>Determine Interdependence"]
  D & E --> F["Computational Process:<br>Compare Persistence Diagrams<br>Test Sector/Market Causality"]
  F --> G["Key Findings:<br>1. Topological Divergence (WD Spikes)<br>2. Bidirectional Causality during Crash<br>3. Stock→Commodity info flow"]

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0 of 67 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.