Accurate determination of time delay and embedding dimension for state space reconstruction from a scalar time series

Abstract

A new and accurate method to determine the time delay and embedding dimension for state space reconstruction of a high dimensional system from a scalar time series using time delay embedding is presented. The time delay is obtained to unprecedented accuracy by evaluating the minima of a newly defined dimension deviation function. The efficacy of our method is tested by applying it to the Lorenz system and the Mackey-Glass system. A good agreement is obtained between the shape and embedding dimension of the physical system attractor(s) and the corresponding reconstruction(s) for both the systems studied. This, along with a heuristic argument provide a validation of the proposed method.