WIAS Preprint No. 2736, (2020)

Iterated-sums signature, quasi-symmetric functions and time series analysis


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

2010 Mathematics Subject Classification

  • 60L10 60L70


  • Shuffle and quasi-shuffle Hopf algebras, half-shuffles, iterated integral- and sum-signatures, quasi-symmetric functions, Hoffmans's exponential




We survey and extend results on a recently defined character on the quasi-shuffle algebra. This character, termed iterated-sums signature, appears in the context of time series analysis and originates from a problem in dynamic time warping. Algebraically, it relates to (multidimensional) quasisymmetric functions as well as (deformed) quasi-shuffle algebras.

Appeared in

  • Sem. Lothar. Combin., 84B (2020), pp. 86/1--86/12.

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