  The stationary statistical properties of independent, identically distributed
(i.i.d.) input symbols provide insights on the induced nonlinear interference
(NLI) during fiber transmission. For example, kurtosis is known to predict the
modulation format-dependent NLI. These statistical properties can be used in
the design of probabilistic amplitude shaping (PAS), which is a popular scheme
that relies on an amplitude shaper for increasing spectral efficiencies of
fiber-optic systems. One property of certain shapers used in PAS -- including
constant-composition distribution matchers -- that is often overlooked is that
a time-dependency between amplitudes is introduced. This dependency results in
symbols that are non-i.i.d., which have time-varying statistical properties.
Somewhat surprisingly, the effective signal-to-noise ratio (SNR) in PAS has
been shown to increase when the shaping blocklength decreases. This blocklength
dependency of SNR has been attributed to time-varying statistical properties of
the symbol sequences, in particular, to variation of the symbol energies. In
this paper, we investigate the temporal energy behavior of symbol sequences,
and introduce a new metric called energy dispersion index (EDI). EDI captures
the time-varying statistical properties of symbol energies. Numerical results
show strong correlations between EDI and effective SNR, with absolute
correlation coefficients above 99% for different transmission distances.
