Nonlinear Prediction in Complex Systems Using the Ruelle-Takens Embedding

Abstract

We exploit ideas of nonlinear dynamics in a complex non-deterministic dynamical setting. Our object of study is the observed riverflow time series of the Portuguese Paiva river whose water is used for public supply. The Ruelle-Takens delay embedding of the daily riverow time series revealed an intermittent dynamical behavior due to precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbor method of prediction revealed good predictability in the laminar regime, but we warn that this method is misleading in the presence of rain. We present some new insights between the quality of the prediction in the laminar regime, the embedding dimension, and the number of nearest neighbors considered.