long-range correlations and trends between consecutive earthquakes

One of the most interesting properties that time series of different kind of phenomena exhibit, is the long-range correlation, also known as long memory or long-range persistence, means that the auto-covariance function decays exponentially, by a spectral density that tends to infinity (bardet et al., 2003; cajueiro & tabak, 2004). self-similar processes have been used successfully to model data exhibiting long memory and arising in a wide variety of fields, ranging from physics (geophysics, turbulence, hydrology, solid-state physics, …) or biology (dna sequences, heat ratevariability, auditory nerves spike trains, …), to human operated systems (telecommunications network traffic, image processing, pattern recognition, finance, …).