Multi-Scaling Comparative Analysis of Time Series and a Discussion on "Earthquake Conversations" in California

Time series are characterized by complex memory and/or distribution patterns. In this letter we show that models obeying to different statistics may equally reproduce some pattern of a time series. In particular we discuss the difference between Lévy-walk and fractal Gaussian intermittent signals and show that the adoption of complementary scaling analysis techniques may be useful to distinguish the two cases. Finally, we apply this methodology to the earthquake occurrences in California and suggest the possibility that earthquake occurrences are described by a \textit{colored} (= `long-range correlated') Generalized Poisson model.