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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Physics

• Full title: Fractal and Diffusion Entropy Analysis of Time Series
• Subtitle: Theory, concepts, applications and computer codes for studying fractal noises and Lévy walk signals
• Author: Nicola Scafetta
• Language: English
• Binding: Paperback
• Number of pages: 300
• EAN: 9783639257953
• ISBN: 3639257952
• ID: 06833209
• Publisher: VDM Verlag
• Weight: 470 g
• Dimensions: 228 × 153 × 19 mm
• Date of publishing: 28. May 2010

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