Fractal and Diffusion Entropy Analysis of Time Series (Paperback) (ISBN-13: 9783639257953)

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: Nicola Scafetta
ISBN-10: 3639257952
ISBN-13: 9783639257953
Publisher: VDM Verlag
Language: English
Published: 05/28/2010
Pages: 300
Format: Paperback
Weight: 0.97lbs
Size: 9.00h x 6.00w x 0.67d