  In data science, one is often confronted with a time series representing
measurements of some quantity of interest. Usually, as 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.
