20 years of ordinal patterns: Perspectives and challenges

Abstract

In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as ordinal patterns) which are defined in terms of the temporal ordering of data points in a time series, and whose probabilities are known as ordinal probabilities. With the ordinal probabilities, the Shannon entropy can be calculated, which is the permutation entropy. Since it was proposed, the ordinal method has found applications in fields as diverse as biomedicine and climatology. However, some properties of ordinal probabilities are still not fully understood, and how to combine the ordinal approach of feature extraction with machine learning techniques for model identification, time series classification or forecasting remains a challenge. The objective of this perspective article is to present some recent advances and to discuss some open problems.

Accepted in EPL

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Cited by in corpus (9)

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• Identifying and anticipating the threshold bifurcation of a complex laser with permutation entropy
• Markov-modulated model for landing flow dynamics: An ordinal analysis validation
• Quantifying deviations from Gaussianity with application to flight delays distributions
• Including the magnitude variability of a signal into the ordinal pattern analysis
• Transcript-based estimators for characterizing interactions
• Exploring the robustness of permutation entropy analysis to differentiate between closed-eyes and open-eyes resting states
• Permutation-Based Distances for Groups and Group-Valued Time Series