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Universitat de Barcelona (24/04/2009), Conrad Perez; Antonio Turiel (Dir.)
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A microcanonical cascade formalism for multifractal systems and its application to data inference and forecasting
Oriol Pont1

Many 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 field. 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 appro- priate algorithms to achieve this purpose remains a major challenge, since discretization, gaps, noise and long-range correlations require ad- vanced 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 appropri- ate selection of the representation basis, we greatly improve inference capabilities in a robust fashion. In addition, we show two applications of microcanonical cascades: first, forecasting of stock market series; and second, detection of interscale heat transfer in the ocean.
1:  UB - Universitat de Barcelona
multiplicative cascade – data inference

Many 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 field. 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 appro- priate algorithms to achieve this purpose remains a major challenge, since discretization, gaps, noise and long-range correlations require ad- vanced 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 appropri- ate selection of the representation basis, we greatly improve inference capabilities in a robust fashion. In addition, we show two applications of microcanonical cascades: first, forecasting of stock market series; and second, detection of interscale heat transfer in the ocean.

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