The series formed by time intervals between particle detections are generated by using the model wherein increasing and decreasing probabilities of particle number in a very short time interval are equivalent. These have 1/f spectra in a similar way to the series generated in the author's previous work by using the branching process model. The self-correlation function between the detections, however, behaves in a different way from that expected from a series with a pure 1/f spectrum. Owing to the anomalously large power spectral density at f=1, the correlation function behaves as mu ^alpha, where mu is a count difference between two detections.