extension of estimate_delay to forward, backward and mixed delays as in Schumann-Bisschoff, Parlitz et al.

[finmod]

The state-of-the-art inspiration to estimate_delay is nicely condensed in the thesis of Jan Schumann-Bischoff which you can find here: https://d-nb.info/1116709740/34. Chapter 9 on the Shinriki oscillator has all the ingredients of a good benchmark for all of these delay, reconstruction and prediction methods. It also extends to state and parameter estimation for a system of three timeseries and 9 parameters.

In Julia, forward diff is considered efficient whereas backward diff may be more problematical.

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[ChrisRackauckas]

In Julia, forward diff is considered efficient whereas backward diff may be more problematical.

Backwards diff is fine these days. It'll be nice to have Capstan.jl completed, but it's really not necessary and there's no need to avoid ReverseDiff.jl these days.