Wavelet-based Fano factor for long-range dependent point processes

Time-series recorded in a large number of biological phenomena, like the auditory nerve fiber response, can efficiently be modeled by long-range dependent point processes. The resulting slowly (power-law) decreasing autocorrelation can efficiently be revealed when studying the process over larger and larger scales of time. This was the key idea of the Fano factor, which measures the variance of the number W of events within a window of length T. The long-range dependence in random point processes is usually tested by using the so-called Fano factor. Here, it is shown how this classical method can be generalized and made more versatile by using explicitly a multiresolution approach based on wavelets