WIAS Preprint No. 2795, (2020)

Generalized iterated-sums signatures


  • Diehl, Joscha
  • Ebrahimi-Fard, Kurusch
  • Tapia, Nikolas
    ORCID: 0000-0003-0018-2492

2010 Mathematics Subject Classification

  • 60L10 60L70 16Y60


  • Time series analysis, time warping, signature, quasi-shuffle product, Hoffman`s exponential, Hopf algebra




We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F. Király and H. Oberhauser. In particular, we show how to recover the character property of the associated linear map over the tensor algebra by considering a deformed quasi-shuffle product of words on the latter. We introduce three non-linear transformations on iterated-sums signatures, close in spirit to Machine Learning applications, and show some of their properties.

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