  We study the power density spectrum (PDS) of light curves of the observed
gamma-ray bursts (GRBs) to search for a direct signature for cosmological time
dilation in the PDS statistics with the GRBs whose redshifts $z$'s are known.
The anticorrelation of a timescale measure and a brightness measure is indirect
evidence of its effect. On the other hand, we directly demonstrate that a time
dilation effect can be seen in GRB light curves. We find that timescales tend
to be shorter in bursts with small redshift, as expected from cosmological
time-dilation effects, and we also find that there may be non-cosmological
effects constituting to this correlation. We discuss its implication on
interpretations of the PDS analysis results. We put forward another caution to
this kind of analysis when we statistically exercise with GRBs whose $z$ is
unknown.
