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A microcanonical cascade formalism for multifractal systems and its application to data inference and forecasting

AuthorsPont, Oriol
AdvisorPérez-Vicente, Conrad J.; Turiel, Antonio
Issue Date2009
PublisherUniversidad de Barcelona
AbstractMany complex systems in Nature are multifractal, a feature closely related to scale invariance. Multifractality is ubiquitous and so it can be found in systems as diverse as marine turbulence, econometric series, heartbeat dynamics and the solar magnetic eld. In recent years, there has been growing interest in modelling the multifractal structure in these systems. This has improved our understanding of certain phenomena and has opened the way for applications such as reduction of coding redundancy, reconstruction of data gaps and forecasting of multifractal variables. Exhaustive multifractal characterization of experimental data is needed for tuning parameters of the models. The design of appropriate algorithms to achieve this purpose remains a major challenge, since discretization, gaps, noise and long-range correlations require advanced processing, especially since multifractal signals are not smooth: due to scale invariance, they are intrinsically uneven and intermittent. In the present study, we introduce a formalism for multifractal data based on microcanonical cascades. We show that with appropriate selection of the representation basis, we greatly improve inference capabilities in a robust fashion. In addition, we show two applications of microcanonical cascades: rst, forecasting of stock market series; and second, detection of interscale heat transfer in the ocean
DescriptionMemoria de tesis doctoral presentada por Oriol Pont i Pla para optar al grado de Doctor por la Universitat de Barcelona (UB), realizada bajo la dirección del Dr. Conrad J. Pérez-Vicente y del Dr. Antonio Turiel Martínez del Institut de Ciències del Mar (ICM-CSIC).-- 126 pages
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