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

TL;DR

This paper compares different statistical models for time series, emphasizing the importance of multiple scaling techniques to distinguish them, and applies this approach to analyze earthquake data in California, proposing a long-range correlated Poisson model.

Contribution

It introduces a multi-scaling analysis framework to differentiate between Lévý-walk and fractal Gaussian signals and applies it to earthquake data, suggesting a new model for earthquake occurrences.

Findings

Different models can reproduce similar time series patterns.

Complementary scaling techniques help distinguish underlying processes.

Earthquake data may be described by a long-range correlated Poisson model.

Abstract

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 L\'evy-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.