Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918165515075584 |
|---|---|
| author | de Jeneret, Pattravadee de Favereau Diamantis, Ioannis |
| author_facet | de Jeneret, Pattravadee de Favereau Diamantis, Ioannis |
| contents | This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study de Jeneret, Pattravadee de Favereau Diamantis, Ioannis Machine Learning General Economics Economics Applications 55N31, 62H30, 91B84, 91G70, 68T09 G.2.3; I.5.3; I.5.4 This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. 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. |
| title | Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study |
| topic | Machine Learning General Economics Economics Applications 55N31, 62H30, 91B84, 91G70, 68T09 G.2.3; I.5.3; I.5.4 |
| url | https://arxiv.org/abs/2510.19306 |