Fractal and Diffusion Entropy Analysis of Time Series: Theory, concepts, applications and computer codes for studying fractal noises and Lévy walk signals - Softcover

Scafetta, Nicola

Softcover

ISBN 10: 3639257952 ISBN 13: 9783639257953

Publisher: VDM Verlag Dr. Müller, 2010

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.

About this title

About the Author

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.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2010
• Language: English
• ISBN 10: 3639257952
• ISBN 13: 9783639257953
• Binding: Paperback
• Number of pages: 300