  We calculate the real and non-statistical higher moment excitation functions
($\sqrt{s_{NN}}$ = 11.5 to 200 GeV) for the net-proton, net-baryon, and the
net-charge number event distributions in the relativistic Au+Au collisions with
the parton and hadron cascade model PACIAE. It turned out that because of the
statistical fluctuation dominance it is very hard to see signature of the CP
singularity in the real higher moment excitation functions. It is found that
the property of higher moment excitation functions are significantly dependent
on the window size, and hence the CP signatures may show only in a definite
window for a given conserved observable non-statistical higher moments. But for
a given widow size, the CP singularity may show only in the non-statistical
higher moment excitation functions of a definite conserved observable.
