  Delay embedding methods are a staple tool in the field of time series
analysis and prediction. However, the selection of embedding parameters can
have a big impact on the resulting analysis. This has led to the creation of a
large number of methods to optimise the selection of parameters such as
embedding lag. This paper aims to provide a comprehensive overview of the
fundamentals of embedding theory for readers who are new to the subject. We
outline a collection of existing methods for selecting embedding lag in both
uniform and non-uniform delay embedding cases. Highlighting the poor dynamical
explainability of existing methods of selecting non-uniform lags, we provide an
alternative method of selecting embedding lags that includes a mixture of both
dynamical and topological arguments. The proposed method, {\em Significant
Times on Persistent Strands} (SToPS), uses persistent homology to construct a
characteristic time spectrum that quantifies the relative dynamical
significance of each time lag. We test our method on periodic, chaotic and
fast-slow time series and find that our method performs similar to existing
automated non-uniform embedding methods. Additionally, $n$-step predictors
trained on embeddings constructed with SToPS was found to outperform other
embedding methods when predicting fast-slow time series.
