Local fractal analysis of noise-like time series by all permutations method
2014jgx | Panchelyuga V.A., Panchelyuga M.S.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics of the Russian Academy of Sciences, Pushchino, Russia, panvic333@yahoo.com

In the present work local fractal analysis of non-stationary time series by all permutations method (APM) is developed. APM-method [1] incorporates ideas of method of minimal cover [2] and histograms method [1]. Analysis of histograms method achieves that some periods in noise-like time series can be revealed only by means of the method and cannot be find out by traditional methods of time series analysis like correlation analysis, spectral analysis, dispersion analysis and so on. Connection between shapes of smoothed histograms constructed on the base of short segments of time series of fluctuations and fractal dimension of the segments is studied. Is shown that fractal dimension posses all main properties of histogram method. On this base a further development of fractal dimension determination algorithm is proposed. This algorithm allows precision determination of fractal dimension by using short (30-60 points) time series segments. This property of APM-method leads to possibility of analysis of non-stationary time series.

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