Initializing a flicker-noise generator

The Barnes-Jarvis flicker-noise generator is usually initialized by setting its filter variables to zero. Call the resulting output y
p
One can also initialize the filter so that the output is a stationary process y
s
. Let these outputs represent clock-frequency deviations. Then, although y
s
and y
p
cannot be distinguished by their two-sample variances, the mean square time-interval error of y
s
, exceeds that of y
p
by a factor of the order log t.