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Published in:
The Complex Geometry of the Mandelbrot Set Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Modeling Financial Time Series: Multifractal Cascades and Rényi Entropy

Authors : Petr Jizba, Jan Korbel

Published in: ISCS 2013: Interdisciplinary Symposium on Complex Systems

Publisher: Springer Berlin Heidelberg

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Abstract

We show that a number of realistic financial time series can be well mimicked by multiplicative multifractal cascade processes. The key observation is that the multi-scale behavior in financial progressions fits well the multifractal cascade scaling paradigm. Connections with Kolmogorov’s idea of multiplicative cascade of eddies in the well developed turbulence are briefly discussed. To put some flesh on a bare bones we compare volatility time series for S&P 500 stock index with a simulated multiplicative multifractal cascade processes. Qualitative agreement is surprisingly good. Salient issues, such as Codimension functions or Multifractal Diffusion analysis and its role in scaling identification are also discussed.

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previous chapter Analyses of the Chaotic Behavior of the Electricity Price Series
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Footnotes
1
We shall note that for \(q<0\) the definition of entropy can be problematic (e.g. can exhibit instabilities, see e.g. Ref. [12]), and therefore shall deal only with \(q \ge 0\).
 
Literature
1.
2.
Hentschel, H., Procaccia, I.: The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8, 435–444 (1983)CrossRefMATHMathSciNet
3.
Harte, D.: Multifractals: theory and application. Chapmann & Hall/CRC, Boca Raton (2001)
4.
Koscielny-Bunde, E., Kantelhardt, J., Braun, P., Bunde, A., Havlin, S.: Long-term persistence and multifractality of river runoff records: detrended fluctuation studies. J. Hydrol. 322, 120–137 (2006)CrossRef
5.
Klafter, J., Lim, S.L., Metzler, R.: Fractional Dynamics. Imperial College Press, London (2011)
6.
Peng, C.K., Buldyrev, S., Havlin, S., Simons, M., Stanley, H., Goldbergerz, A.: Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689 (1994)CrossRef
7.
Lovejoy, S., Schertzer, D.: The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge University Press, Cambridge (2013)
8.
Mandelbrot, B., Calvet, L., Fisher, A.: A multifractal model of asset returns. (Cowles Foundation Discussion Papers)
9.
Mandelbrot, B.: Multifractals and 1/f Noise: Wild Self-Affinity in Physics (1963–1976). Springer, New York (1999)
10.
Kantelhardt, W., Zschiegner, S., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.: Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316, 87–114 (2002)CrossRefMATH
11.
Morales, R., Di Matteo, T., Gramatica, R., Aste, T.: Dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series. Physica A: Stat. Mech. Appl. 391, 3180–3189 (2012)CrossRef
12.
13.
Huang, J., et al.: Multifractal diffusion entropy analysis on stock volatility in financial markets. Physica A 391, 5739–5745 (2012)CrossRef
14.
Jizba, P., Kleinert, H., Shefaat, M.: Rényi information transfer between financial time series. Physica A 391, 2971–2989 (2012)CrossRef
15.
Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., Marsan, D.: Multifractal cascade dynamics and turbulent intermittency. Fractals 5, 427–471 (1997)CrossRefMATHMathSciNet
16.
Mandelbrot, B.: Heavy tails in finance for independent or multifractal price increments. In Rachev, S.T. (ed.) Handbook of Heavy Tailed Distributions in Finance. Elsevier, Amsterdam (2003)
17.
Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluids at very large reynolds numbers. Dokl. Akad. Nauk SSSR. 32, 16–18 (1941)MATH
18.
Tessier, Y., Lovejoy, S., Schertzer, D.: Universal multifractals: theory and observations for rain and clouds. J. Appl. Meteorol. 32, 223–223 (1993)CrossRef
19.
Muzy, J.F., Bacry, E., Arneodo, A.: Multifractal formalism for fractal signals: the structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E 47, 875 (1993)CrossRef
20.
Calvet, L., Fisher, A.: Multifractal Volatility: Theory Forecasting and Pricing. Academic Press, Amsterdam (2008)
Metadata
Title
Modeling Financial Time Series: Multifractal Cascades and Rényi Entropy
Authors
Petr Jizba
Jan Korbel
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
ISCS 2013: Interdisciplinary Symposium on Complex Systems

Print ISBN: 978-3-642-45437-0

Electronic ISBN: 978-3-642-45438-7

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-642-45438-7_22

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