Abstract
Complex non-linear time series are ubiquitous in geosciences. Quantifying complexity and non-stationarity of these data is a challenging task, and advanced complexity-based exploratory tool are required for understanding and visualizing such data. This paper discusses the Fisher-Shannon method, from which one can obtain a complexity measure and detect non-stationarity, as an efficient data exploration tool. The state-of-the-art studies related to the Fisher-Shannon measures are collected, and new analytical formulas for positive unimodal skewed distributions are proposed. Case studies on both synthetic and real data illustrate the usefulness of the Fisher-Shannon method, which can find application in different domains including time series discrimination and generation of times series features for clustering, modeling and forecasting. The paper is accompanied with Python and R libraries for the non-parametric estimation of the proposed measures.
Highlights
The ubiquity and extensive growth of available temporal data requires the development of reliable techniques to extract knowledge from them and to understand multifaceted time-dependent phenomena
The joint Fisher information measure (FIM)/Shannon entropy power (SEP) analysis has been used as a statistical complexity measure, albeit there is no clear consensus about the definition of signal complexity (Esquivel et al, 2010)
Analyzing the results obtained from the data without noise, it is easy to see how the SEP, FIM and Fisher-Shannon complexity (FSC) peak occurrences correspond to dynamic changes shown by the bifurcation diagram and the Lyapunov exponent
Summary
The ubiquity and extensive growth of available temporal data requires the development of reliable techniques to extract knowledge from them and to understand multifaceted time-dependent phenomena. Following Frieden work, FIM has found applications in non-linear time-series analysis. Telesca et al (2015a) proposed a classifier of (non-)tsunamigenic potential of earthquake build on several time series features, including FIM, SEP, FSC. The same authors studied yearly variation of the FIM, the SEP and the FSC on wind measurements (Telesca and Lovallo, 2013). Presenting some new theoretical results on FIM and SEP, developing operational FIM and SEP tools for the nonlinear time-series analysis, demonstrating through two case studies, based on simulated (chaotic) and real data (high frequency wind speed measurements), the efficiency and usefulness of the proposed methods.
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