Optimal time delay embedding for nonlinear time series modeling

TL;DR

This paper introduces a new method for selecting optimal non-uniform time delays in embedding for nonlinear time series modeling, improving prediction accuracy and realism over standard methods.

Contribution

It proposes a novel, computationally efficient technique to quantify and select the best set of time delays for nonlinear time series embedding.

Findings

More realistic dynamics in reconstructed systems

Improved prediction accuracy over standard embeddings

Effective in diverse experimental and simulated systems

Abstract

When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in the time delay embedding. We propose a new technique which can quantify the suitability of a particular set of variables and we suggests a computationally efficient scheme to determine the best non-uniform time delay embedding for modeling of time series. Our results are based on the assumption that, in general, the variables which give the best local constant model will also give the best nonlinear model. In a wide variety of experimental and simulated systems we find that this method produces dynamics that are more realistic and predictions that are more accurate than standard uniform embeddings.