Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions

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