Fractal and Diffusion Entropy Analysis of Time Series: Theory, concepts, applica

Description: Fractal and Diffusion Entropy Analysis of Time Series by Nicola Scafetta 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Author Biography Nicola Scafetta, Ph. D.: Studied statistical physics and complex systems at the University of North Texas (USA). Laurea in Physics from the University of Pisa (Italy). Research scientist at Duke University, Durham NC. Details ISBN3639257952 Author Nicola Scafetta Short Title FRACTAL & DIFFUSION ENTROPY AN Pages 300 Publisher VDM Verlag Language English ISBN-10 3639257952 ISBN-13 9783639257953 Media Book Format Paperback Year 2010 Publication Date 2010-05-28 Subtitle Theory, concepts, applications and computer codes for studying fractal noises and LÃ©vy walk signals UK Release Date 2010-05-28 Imprint VDM Verlag Country of Publication Germany Illustrations Illustrations, black and white Audience General We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:132590542;

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