Characterizing the statistical complexity of nonlinear time series via ordinal pattern transition networks

Complex network approaches have lately emerged as innovative and complementary notions of nonlinear time series analysis, capable of revealing numerous aspects that more classic analytic methods fail to reveal. In this paper, we concentrate on ordinal pattern transition networks (OPTN) to characterize the statistical complexity of time series by considering each pattern as a network node and the probability of transition between patterns as a directed weighted edge between nodes. The traditional complexity measures of time series, permutation entropy (PE) and transition entropy (TE), have been first explained via OPTN, and a new statistical complexity technique termed permutation weighted statistical transition entropy (PWSTE) is suggested to address some drawbacks of some existing complexity measures. In the context of OPTN, the proposed PWSTE enhances PE and TE by taking into account both static information (i.e., network node probability distributions) and dynamic information (i.e., time series transition probabilities represented by nodes). It combines with the imbalance of OPTN, which enables a more accurate measurement of the statistical complexity of nonlinear time series. The suggested new technique for assessing statistical complexity is thoroughly described based on the simulated time series, and the findings demonstrate that the proposed algorithm is more sensitive and effective in identifying dynamic changes. When the proposed algorithm is used to medical data, the EEG time series of epileptic patients are examined to define the changes in EEG data over various stages. The findings demonstrate that the proposed PWSTE algorithm outperforms conventional methods in identifying the stage in which a patient’s EEG data is located.