{"product_id":"multi-fractal-stochastic-modeling-of-the-auroral-electrojet-index-von-martin-sund","title":"Multi-fractal Stochastic Modeling of the Auroral Electrojet Index","description":"\u003cp\u003eIn this thesis we have analyzed the Auroral  Electrojet (AE) Index over the years 2000 to 2005, a time series consisting of over 3 000  000 data points. This data is described as a multi- fractal stochastic process. We first introduce a  class of random multiplicative measures, which provide the  multi-fractality in the stochastic processes. We also review  the theory of fractal dimensions and scaling functions, before introducing the  Multifractal Model of Asset Returns (MMAR), [15]. The scaling properties of various versions of the  MMAR model are compared with the scaling function of the AE Index, and through  this we describe the multi-fractal properties of the AE Index. Additionally, we have studied probability density  functions (pdf) at different time scales, and used this to compare the stochastic  models with the AE data. Finally we have tested our diagnostic tools on  simulated multi-fractal models. These experiments show that the methods are capable of  detecting multi-fractality.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838381527\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838381527","offer_id":39469262831709,"sku":"9783838381527","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/52bba71a-4f15-4511-a1fa-99a033052569.jpg?v=1758174572","url":"https:\/\/shop.autorenwelt.de\/products\/multi-fractal-stochastic-modeling-of-the-auroral-electrojet-index-von-martin-sund","provider":"Autorenwelt Shop","version":"1.0","type":"link"}