{"product_id":"fractal-and-diffusion-entropy-analysis-nicola-scafetta-9783639257953","title":"Fractal and Diffusion Entropy Analysis of Time Series","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Nicola Scafetta\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3639257952\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783639257953\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e VDM Verlag\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/28\/2010\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 300\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.97lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.67d","brand":"Nicola Scafetta","offers":[{"title":"Paperback","offer_id":47305529098495,"sku":"9783639257953","price":85.32,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_a2874f73-944c-4cfe-b00a-1f3383ddada4.jpg?v=1758831132","url":"https:\/\/www.whiterainbookhouse.com\/products\/fractal-and-diffusion-entropy-analysis-nicola-scafetta-9783639257953","provider":"WR Book House","version":"1.0","type":"link"}