This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Diehl, JoschaKurusch, Ebrahimi-FardTapia, Nikolas2022-06-232022-06-232019https://oa.tib.eu/renate/handle/123456789/9187https://doi.org/10.34657/8225In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants.We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties.eng510Time series analysistime-warping invariantssignaturequasisymmetric functionsquasi-shuffle productHoffman's exponentialarea-operationHopf algebraReport23 S.