I'm interested in exploring some time series from the point of view of a delay embedding and Taken's theorem. All the examples I have seen of time delay embedding involve regularly (evenly) sampled time series where lagged versions of the observed series can easily be created.
However, I am interested in time series that are irregularly sampled in time. By this I mean observations are not at integer time points with perhaps some missing observations, but as observations of a continuous process taken at irregular intervals.
Is there a way to create a time delay embedding of such irregular time series? If there are, can such embeddings be used in the context of Taken's theorem?
As usual, the answer is "it depends".
There are some generalizations of Takens that obviate the need for regularly sampled time series, by using multi-dimensional time series (see Sauer et al. 1991, Stark et al. 1997, Stark et al. 2003, Deyle & Sugihara 2011).
Alternatively, if the data are only a "little" irregularly sampled, then you might be able to treat it as process error. I recommend Casdagli et al. 1991 as an excellent reference on this topic.
For anything fancier, maybe contact me and we can write a paper together. ;)