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

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