Applications of Multifractal Diffusion Entropy Analysis to Daily and Intraday Financial Time Series

  • Petr JizbaEmail author
  • Jan Korbel
Part of the Emergence, Complexity and Computation book series (ECC, volume 14)


Scaling properties and fractal structure are one of the most important aspects of real systems that point to their complexity. These properties are closely related to the theory of multifractal systems and theory of entropy. Estimation of scaling (or multifractal) exponents belongs to the essential techniques that can reveal complexity and inner structure of the system. To successful techniques belongs Multifractal diffusion entropy analysis, based on estimation of Rényi entropy of the system. In the recent article [1], we have discussed one possible method of estimation Rényi entropy from proper estimation of underlying probability histograms. In Ref. [2], we have applied the method to daily and intraday financial data in order to test the stability of the system. This article summarizes existing progress in this field and shows the robustness of the method on high-frequency financial data.


Financial time series Rényi entropy Multifractal analysis 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePragueCzech Republic
  2. 2.Institute for Theoretical PhysicsFreie Universität BerlinBerlinGermany
  3. 3.Max-Planck-Institute for the History of ScienceBerlinGermany

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