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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?

Gavin Simpson
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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. ;)

Hao Ye
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