Complexity-based permutation entropies: From deterministic time series to white noise

This is a paper in the intersection of time series analysis and complexity theory that presents new results on permutation general entropy particular. In this context, refers to characterization by means ordinal patterns (permutations), entropic measures, decay rates missing patterns, more. Since inception \textquotedblleft ordinal\textquotedblright\ methodology, its practical application any type scalar real-valued processes have proven be simple useful. However, theoretical aspects remained limited noiseless deterministic dynamical systems, main obstacle being super-exponential growth visible permutations with length when randomness (also form observational noise) present data. To overcome difficulty, we take approach through classes, which are precisely defined length, regardless or noisy nature We consider three major classes: exponential, sub-factorial factorial. The next step adapt concept Z-entropy each those call because it coincides conventional exponential class. Z-entropies family group entropies, them extensive given result unified random processes, from systems white noise, concepts tools. Numerical simulations show discriminates all classes.