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arXiv · 2009.08443

Tropical time series, iterated-sums signatures and quasisymmetric functions

Joscha Diehl·Kurusch Ebrahimi-Fard·Nikolas Tapia
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Abstract

Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of (real-valued) time series that are not easily available using existing signature-type objects. We demonstrate how the signature extracts chronological aspects of a time series, and that its calculation is possible in linear time. We identify quasisymmetric expressions over semirings as the appropriate framework for iterated-sums signatures over semiring-valued time series.

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Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia. 2020-09-17. Tropical time series, iterated-sums signatures and quasisymmetric functions. https://doi.org/10.1137/20m1380041

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