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Fractal and Diffusion Entropy Analysis of Time Series

by Nicola Scafetta
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Current price ₹7,310.00
Original price ₹8,295.00
Original price ₹8,295.00
Original price ₹8,295.00
(-12%)
₹7,310.00
Current price ₹7,310.00

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Book cover type: Paperback
  • ISBN13: 9783639257953
  • Binding: Paperback
  • Subject: N/A
  • Publisher: VDM Verlag
  • Publisher Imprint: VDM Verlag
  • Publication Date:
  • Pages: 300
  • Original Price: GBP 65.57
  • Language: English
  • Edition: N/A
  • Item Weight: 440 grams
  • BISAC Subject(s): Physics / General

Scale invariance has been found to empirically hold for a number of complex systems. The correct evaluation of the scaling exponents of a time series is fundamental to assess the real physical nature of a phenomenon. The traditional methods used to determine these scaling exponents are equivalent because they all rely on the numerical evaluation of the variance. However, two statistical classes of phenomena exist: fractal Brownian motions and Lévy flights and walks. In this book I present the theory and concepts of alternative fractal methods of time series analysis. I introduce a complementary method based on the Shannon entropy: the Diffusion Entropy Analysis (DEA). Using synthetic, solar, geophysical, sociological, physiological and biological data, I examine the properties of these methodologies and discuss the physical ambiguities of the variance-based methods. I argue that the variance-based algorithms should be used together with DEA to properly distinguish fractal Brownian motions from Lévy flight-walk classes of noises and complex processes. Computer C++ codes are provided for generating complex fractal noises and performing multiple fractal analyses of time series.

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