Causality Analysis of COVID-19 Induced Crashes in Stock and Commodity Markets: A Topological Perspective

TL;DR

The paper tackles the detection and characterization of COVID-19–induced crashes in US stock and commodity markets, along with sector-level interdependencies, by applying Topological Data Analysis to multidimensional time-series. It integrates persistence diagrams and Wasserstein distances with Granger-causality to identify topological crashes, compare market topologies, and infer directional information flow across periods. The study demonstrates that WD spikes reliably signal crashes, reveals significant topological differences between stock and commodity markets during crises, and uncovers bidirectional causal interplay during the crash period with stock generally dominating outside crisis windows. The methodology offers a robust framework for monitoring market interconnectedness and potential crash precursors, with practical implications for risk management and cross-asset/sector analysis.

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.

Figures (9)

• Figure 1: Figures depict the Rips complex for the example dataset at various resolutions($\varepsilon$). Figs. (a),(b),(c) and (d) represent the Rips complex at $\varepsilon= 0,0.5,2$ and $2.7$ respectively.
• Figure 2: Presistence diagram for $0$-dimensional homology group for the example dataset
• Figure 3: Figures depict the Wasserstein distance matching between persistence diagrams. The blue points correspond to PD1 and the red points correspond to PD2. Fig. (a) represents the comparison of PD1 points with the positive diagonal. Fig. (b) represents the comparison of PD1 with the PD2 points. Each solid green line represents the optimal matching for the corresponding point(s).
• Figure 4: Plot (a) represents the degree-1 Wasserstein distance and plot (b) represents degree-2 Wasserstein distances in the Stock market. Both plots display abrupt spikes during the COVID-19 pandemic indicated by a red box.
• Figure 5: Plot (a) represents the degree-1 Wasserstein distance and plot (b) represents degree-2 Wasserstein distances in the commodity market. Both plots display abrupt spikes during the COVID-19 pandemic indicated by a red box.