Statistics and contrasts of order patterns in univariate time series

Quantifying the diversity of multiple time series with an ordinal symbolic approach

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.

Discrete-Valued Time Series

Time series are sequentially observed data in which important information about the phenomenon under consideration is contained not only in the individual observations themselves, but also in the way these observations follow one another [...].

Two new parameters for the ordinal analysis of images

Local patterns play an important role in statistical physics as well as in image processing. Two-dimensional ordinal patterns were studied by Ribeiro et al. who determined permutation entropy and complexity in order to classify paintings and images of liquid crystals. Here, we find that the 2 × 2 patterns of neighboring pixels come in three types. The statistics of these types, expressed by two parameters, contains the relevant information to describe and distinguish textures. The parameters are most stable and informative for isotropic structures.