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Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis that are able to unveil many features that are hidden to more traditional analysis methods. In this work, we focus on one particular approach: the application of ordinal pattern transition networks for characterizing time series data. More specifically, we generalize a traditional statistical complexity measure (SCM) based on permutation entropy by explicitly disclosing heterogeneous frequencies of ordinal pattern transitions. To demonstrate the usefulness of these generalized SCMs, we employ them to characterize different dynamical transitions in the logistic map as a paradigmatic model system, as well as real-world time series of fluid experiments and electrocardiogram recordings. The obtained results for both artificial and experimental data demonstrate that the consideration of transition frequencies between different ordinal patterns leads to dynamically meaningful estimates of SCMs, which provide prospective tools for the analysis of observational time series.
In the past decade, the field of nonlinear time series analysis has been undergoing fast developments benefiting from concepts from complex network theory. Along this line of research, ordinal pattern transition networks have been expanding the established concept of ordinal time series analysis and provide new insights into the dynamical organization underlying time series data that complement existing methods like permutation entropy. Permutation based on ordinal patterns is a simple and easy to implement concept that naturally provides statistical complexity measures (SCMs), which in the case of permutation entropy relies on pattern frequencies only. Yet, much additional information can be exploited by including ordinal pattern transition frequencies into the definitions of SCMs—an idea that, however, has not been widely developed and applied so far. In this work, we generalize existing permutation based SCMs by means of ordinal pattern transition networks that take into account the pattern transition properties explicitly. The usefulness of our generalizations is demonstrated by using time series of both model and experimental data
