A versatile ordinal distance for time series analysis

LUCIANO ZUNINO; FELIPE OLIVARES; HAROLDO V. RIBEIRO; OSVALDO A. ROSSO

Dresden

Workshop; Ordinal methods: Concepts, applications, new developments and challenges (ORPATT22); 2022

Max Planck Institute for the Physics of Complex Systems (MPIPKS)

In this presentation, the permutation Jensen-Shannon distance (PJSD) is introduced. It is a symbolic metric able to quantify the ordinal similarity between two arbitrary time series. Based on the fusion of two well-known concepts, namely, the Jensen-Shannon divergence and the ordinal encoding scheme, the PJSD inherits all the important advantages associated with them: simplicity, low computational cost, noise robustness and wide applicability. Consequently, large amounts of data with outliers and artifacts can be efficiently handled with this quantifier, making it especially suited to deal with the current big data challenges. It is worth emphasizing its versatility, since hypothesis tests related to the nature of an arbitrary time series can be easily carried out by estimating its PJSD to reference time series appropriately generated according to the null model. Several numerical and experimental analyses illustrate this versatility as well as the robustness for characterizing and classifying time series. For all these reasons, the proposed ordinal distance seems to be a promising addition to the repertoire of existing methods for complex signals analysis.