Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912835901063168 |
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| author | Betken, Annika Micali, Giorgio Marín, Manuel Ruiz |
| author_facet | Betken, Annika Micali, Giorgio Marín, Manuel Ruiz |
| contents | We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides a unified framework applicable to arbitrary symmetry tests. We establish asymptotic results for the resulting test statistics under a broad class of stationary processes. Comprehensive experiments on both synthetic and real data demonstrate that the proposed test achieves high sensitivity to structural asymmetries while remaining fully data-driven and computationally efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach Betken, Annika Micali, Giorgio Marín, Manuel Ruiz Statistics Theory We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides a unified framework applicable to arbitrary symmetry tests. We establish asymptotic results for the resulting test statistics under a broad class of stationary processes. Comprehensive experiments on both synthetic and real data demonstrate that the proposed test achieves high sensitivity to structural asymmetries while remaining fully data-driven and computationally efficient. |
| title | Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2601.14223 |