Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series

Ordinal time series analysis

We discuss robust methods of time series analysis which use only comparisons of values and not their actual size. Local and global order structure are defined as matrices or by rank numbers. Local ranks, autocorrelation by Kendall’s tau, and permutation entropy as complexity measure are introduced in such a way that they contain a scale parameter which allows to study time series on different s...

Ordinal Pattern Dependence between hydrological time series

Ordinal Analysis of Time Series

In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the base of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a...

Ordinal analysis of EEG time series

Ordinal time series analysis is a new approach to the qualitative investigation of long and complex time series. The idea behind it is to transform a given time series into a series of ordinal patterns each describing the order relations between the present and a fixed number of equidistant past values at a given time. Here we consider ordinal pattern distributions and some measures derived fro...

Segmentation and classification of time series using ordinal pattern distributions

The distribution of ordinal patterns in time series has been found to reflect important qualitative features of the underlying system dynamics. Abrupt changes in the dynamics typically result in clearly visible differences between the distributions before and after the break. Recurring dynamical regimes can be discovered by classifying the distributions in different parts of the time series. Th...