Tropical time series, iterated-sums signatures and quasisymmetric functions
This work provides a novel framework for time series analysis, potentially benefiting fields like machine learning and data science, though it appears incremental as it builds on existing signature-type objects.
The authors tackled the problem of systematic feature extraction from time series by introducing the iterated-sums signature over arbitrary commutative semirings, with a focus on the tropical semiring, which extracts chronological aspects not easily available with existing methods and can be calculated in linear time.
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.