Permutation Entropy (PE) is a powerful tool for quantifying the
predictability of a sequence which includes measuring the regularity of a time
series. Despite its successful application in a variety of scientific domains,
PE requires a judicious choice of the delay parameter Ï„. While another
parameter of interest in PE is the motif dimension n, Typically n is
selected between 4 and 8 with 5 or 6 giving optimal results for the
majority of systems. Therefore, in this work we focus solely on choosing the
delay parameter. Selecting Ï„ is often accomplished using trial and error
guided by the expertise of domain scientists. However, in this paper, we show
that persistent homology, the flag ship tool from Topological Data Analysis
(TDA) toolset, provides an approach for the automatic selection of Ï„. We
evaluate the successful identification of a suitable Ï„ from our TDA-based
approach by comparing our results to a variety of examples in published
literature