Causality analysis of COVID-19-induced crashes in stock and commodity markets: A topological perspective

In this paper, we present a topology-inspired framework for analyzing the causal behavior of financial markets and sectors, especially during market crises. By utilizing topological data analysis (TDA) on multiple time series, we capture the evolving topological structure of stock and commodity markets through a characteristic measure — the Wasserstein distance ([Formula: see text]) — which reflects the complex interactions among constituent assets. After observing the crashes due to COVID-19 in both markets and sectors, we directly compare the topologies among market and sector pairs. A significant topological difference between the markets (and sectors) during the crash period indicates a possible temporal lag between the change in market dynamics. Hence, we study the Granger-causal relations between the market (and sector) pairs using the TDA-based [Formula: see text]. The results reveal a shift from unidirectional causality (stock [Formula: see text] commodity) in normal periods to bidirectional causality during the crash. Our sectoral analysis reveals a surge in interconnections and reinforcing feedback loops during the crash, with diminished linkages post-crash. This indicates crisis-driven synchronization, heightened interdependence and amplified systemic risk during the crash period. This study demonstrates that TDA, combined with Granger-causality, offers a powerful approach to analyzing inter-market and inter-sector dependencies, detecting shifts in market behavior, and assessing systemic vulnerability for broader markets and sectors.