Multi-fractal stochastic modeling of the auroral electrojet index
AuthorSund, Martin Jong Yul Shon
In 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. The aim is to describe this data as a multi-fractal stochastic process. We first introduce a class of random multiplicative measures, which provide the multi-fractality in the stochastic processes that will be defined later. We also review the theory of fractal dimensions and scaling functions, before introducing the Multifractal Model of Asset Returns (MMAR), Mandelbrot (1997). 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. The results are good if we average over several independent realizations of the processes.
PublisherUniversitetet i Tromsø
University of Tromsø
MetadataShow full item record
Copyright 2009 The Author(s)
The following license file are associated with this item:
Showing items related by title, author, creator and subject.
Structural analysis along seismic profiles trough late-Paleozoic deposits in Billefjorden and Sassenfjorden, Svalbard and their relation to the Billefjorden Fault Zone Kubiak, Agata (Mastergradsoppgave; Master thesis, 2020-11-09)The focus of this thesis is structural analysis of the Billefjorden Fault Zone astride Billefjorden and Sassenfjorden in Spitsbergen, with the use of seismic interpretation combined/aided by geological and bathymetric maps, field observations and well data. The aim is to describe structures and the tectonic development of the study area. The focus is on large tectonic events from Devonian to ...
Engineering methods for enhancing railway geometry and winter road assessment: A safety and maintenance perspective Brustad, Tanita Fossli (Doctoral thesis; Doktorgradsavhandling, 2020-06-22)In many areas around the world there are limited transportation possibilities when travelling between key cities. If these areas also experience demanding weather conditions or geography, getting from A to B, during difficult conditions, is usually not optimal in regards to accessibility, safety, and comfort. Under challenging conditions, two essential elements in strengthening accessibility, safety, ...
Pedersen, Aleksander (Doctoral thesis; Doktorgradsavhandling, 2020-10-20)In applications for technical problems, Geometric modeling and sensor technology are key in both scientific and industrial development. Simulations and visualization techniques are the next step after defining geometry models and data types. This thesis attempts to combine different aspects of geometric modeling and sensor technology as well as to facilitate simulation and visualization. It includes ...