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JuliaDynamics / DelayEmbeddings.jl

Delay coordinates embeddings and optimizing them
MIT License
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[FR] Ragwitz criterion for embedding time #42

Open Datseris opened 4 years ago

Datseris commented 4 years ago

This work: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.65.056201

introduces a method to estimate delay times for embedding, so that the "timeseries prediction" is optimized. @hkraemer have you seen this before? It scans pairs of $d, τ$ to find the pair that minimizes the nonlinear timeseries prediction error.

hkraemer commented 4 years ago

Thanks for sharing @Datseris, I did not know this before. The approach of Uzal et al. also includes the minimization of a prediction error. Specifically, their $E_2$-function does account also for different prediction horizons (and eventually take the average value). Furthermore they discuss, if the minimization of the prediction error also yields a good reconstruction in general (Sect. IV.B, Figs. 8/9). Their proposed cost-function $L_k$ seems to take everything into account. For a similar/related approach to the one of Ragwitz & Kantz (2002) also see this work by Micheal Small & C.K. Tse. - The same critique holds here.