20 years of ordinal patterns: Perspectives and challenges

TL;DR

This paper reviews 20 years of ordinal pattern analysis in time series, discussing its applications, current understanding, and open challenges in integrating with machine learning for improved analysis.

Contribution

It provides a comprehensive overview of the developments, applications, and unresolved issues in ordinal pattern analysis over the past two decades.

Findings

Ordinal analysis has been applied across diverse fields like biomedicine and climatology.

Some properties of ordinal probabilities remain not fully understood.

Integrating ordinal methods with machine learning poses ongoing 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.