{"product_id":"fractal-and-diffusion-entropy-analysis-of-time-series-9783639257953","title":"Fractal and Diffusion Entropy Analysis of Time Series","description":"\u003cp\u003e • Author(s): Nicola Scafetta\u003cbr\u003e • Publisher: VDM Verlag\u003cbr\u003e • Publisher Imprint: VDM Verlag\u003cbr\u003e • BISAC: Physics - General\u003c\/p\u003e\u003cp\u003eScale 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.\u003c\/p\u003e","brand":"VDM Verlag","offers":[{"title":"Paperback","offer_id":46883086041239,"sku":"9783639257953","price":7310.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783639257953.webp?v=1770237859","url":"https:\/\/atlanticbooks.com\/products\/fractal-and-diffusion-entropy-analysis-of-time-series-9783639257953","provider":"Atlantic Books","version":"1.0","type":"link"}