Librería Samer Atenea
Librería Aciertas (Toledo)
Kálamo Books
Librería Perelló (Valencia)
Librería Elías (Asturias)
Donde los libros
Librería Kolima (Madrid)
Librería Proteo (Málaga)
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.
