Topology of currencies: Persistent homology for FX Co-movements: A Comparative clustering study

Pattravadee de Favereau de Jeneret; Ioannis Diamantis; Pattravadee de Favereau de Jeneret; Ioannis Diamantis

doi:10.3934/DSFE.2026007

Data Science in Finance and Economics

2026, Volume 6, Issue 2: 183-211. doi: 10.3934/DSFE.2026007

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Topology of currencies: Persistent homology for FX Co-movements: A Comparative clustering study

Pattravadee de Favereau de Jeneret ¹,
Ioannis Diamantis ^{2
,
,}

1.
Maastricht University, School of Business and Economics, P.O.Box 616, 6200 MD, Maastricht, The Netherlands
2.
Department of Data Analytics and Digitalisation, Maastricht University, School of Business and Economics, P.O.Box 616, 6200 MD, Maastricht, The Netherlands

Received: 23 October 2025 Revised: 13 January 2026 Accepted: 28 January 2026 Published: 13 April 2026
JEL Codes: C38, C63, F31, G15

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviors. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, $k$-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.
- topological data analysis,
- persistent homology,
- currency co-movements,
- clustering,
- Foreign Exchange (FX) market,
- clustering methods,
- wasserstein distance
Citation: Pattravadee de Favereau de Jeneret, Ioannis Diamantis. Topology of currencies: Persistent homology for FX Co-movements: A Comparative clustering study[J]. Data Science in Finance and Economics, 2026, 6(2): 183-211. doi: 10.3934/DSFE.2026007

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Abstract

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviors. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, $k$-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.

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