Markov models from data by simple nonlinear time series predictors in delay embedding spaces

We analyze prediction schemes for stochastic time series data. We propose that under certain conditions, a scalar time series, obtained from a vector-valued Markov process can be modeled as a finite memory Markov process in the observable. The transition rules of the process are easily computed using simple nonlinear time series predictors originally proposed for deterministic chaotic signals. The optimal time lag entering the embedding procedure is shown to be significantly smaller than the deterministic case. The concept is illustrated for simulated data and for surface wind velocity data, for which the deterministic part of the dynamics is shown to be nonlinear.