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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.13377 |
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| _version_ | 1866912702469767168 |
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| author | Bellingeri, Carlo Penaguiao, Raul |
| author_facet | Bellingeri, Carlo Penaguiao, Raul |
| contents | Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their images, the discrete signature varieties. We introduce them and compute their dimension in many cases. From a particular subclass of these varieties, we derive a partial solution to the Chen-Chow theorem for complex-valued time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13377 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete signature varieties Bellingeri, Carlo Penaguiao, Raul Combinatorics Algebraic Geometry Probability 14Q15, 60L70, 17B45 Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their images, the discrete signature varieties. We introduce them and compute their dimension in many cases. From a particular subclass of these varieties, we derive a partial solution to the Chen-Chow theorem for complex-valued time series. |
| title | Discrete signature varieties |
| topic | Combinatorics Algebraic Geometry Probability 14Q15, 60L70, 17B45 |
| url | https://arxiv.org/abs/2303.13377 |