  For the purpose of phase space reconstruction from nonlinear time series,
delay selection is one of the most vital criteria. This is normally done by
using a general measure viz., mutual information (MI). However, in that case,
the delay selection is limited to the estimation of a single delay using MI
between two variables only. The corresponding reconstructed phase space is also
not satisfactory. To overcome the situation, a high-dimensional estimator of
the MI is used; it selects more than one delay between more than two variables.
The quality of the reconstructed phase space is tested by shape distortion
parameter (SD), it is found that even this multidimensional MI sometimes fails
to produce a less distorted phase space. In this paper, an alternative
nonlinear measure cross autocorrelation (CAC) is introduced. A comparative
study is made between the reconstructed phase spaces of a known three
dimensional Neuro dynamical model, Lorenz dynamical model and a three
dimensional food web model under MI for two and higher dimensions and also
under cross auto-correlation separately. It is found that the least distorted
phase space is obtained only under the notion of cross autocorrelation.
