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COMPARATIVE STUDY OF LOCAL FRACTAL ANALYSIS BY ALL PERMUTATIONS METHOD AND PAIRWISE EXPERT HISTOGRAMS COMPARISON ...
2016jgw | V.A. Panchelyuga, M.S. Panchelyuga, V.A. Kolombet, at all.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics RAS, Pushchino, Russia; Chemical and Nuclear Engineering Department, Polytechnic University of Valencia, Spain, panvic333@yahoo.com

The paper deals with the comparative analysis of two methods for local analysis of noise-like time series. One of the methods, a local fractal analysis by all permutations combinations method (APM) [1, 2], has already proven its effectivity as an instrument that allowed authors to reveal a stable frequency structure in time series of the ?-decay rate fluctuations [3, 4]. The second one is a pairwise expert comparison of the smoothed histogram shapes [1-2, 5]. The methods share a set of the properties: invariance under linear transformations (shifts, dilatations, and mirror reflections), the same as invariance with respect to rearrangement of terms in section of time series that bases calculations of the APM dimensions and construction of a smoothed histogram. The analysis showed that 74% of the pairs selected fully automatically by the APM are the same that were selected in course of expert pairwise histogram comparison, while 26% of the ACM selected pairs were never selected by any expert.



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