Initializing a flicker-noise generator

The Barnes-Javis flicker-noise generator is usually initialized by setting its filter variables to zero with the resulting output y_P. One can also initialize the filter so that the output is a stationary process y_s. It is argued that if 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.