Advanced analysis of temporal data using Fisher-Shannon information: theoretical development and application in geosciences

TL;DR

This paper develops and applies the Fisher-Shannon information measure as a powerful tool for analyzing complex, non-linear, and non-stationary time series data in geosciences, with new formulas and software implementations.

Contribution

It introduces new analytical formulas for Fisher-Shannon measures for skewed distributions and demonstrates their application in geosciences through case studies and software tools.

Findings

Effective detection of non-stationarity in time series

Enhanced feature extraction for clustering and forecasting

Validated approach on synthetic and real geoscience data

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.