  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.
