20 years of ordinal patterns: Perspectives and challenges

¹ Universidad Rey Juan Carlos - Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
² Center for Biomedical Technology, Universidad Politécnica de Madrid - 28223 Pozuelo de Alarcón, Madrid, Spain
³ Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB 07122 Palma de Mallorca, Spain
⁴ Department of Physics, Universitat Politecnica de Catalunya - Rambla St. Nebridi 22, Terrassa 08222, Spain
⁵ Instituto de Física, Universidade Federal de Alagoas (UFAL) - Maceió, Alagoas 57072-970, Brasil

^(a) shiau.sean@gmail.com (corresponding author)

Received: 30 March 2022
Accepted: 26 April 2022

Abstract

In 2002, in a seminal article, Bandt and 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 patters) 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.