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Multifractality And Long-Range Dependence Of Asset Returns: The Scaling Behavior Of The Markov-Switching Multifractal Model With Lognormal Volatility Components

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  • RUIPENG LIU

    ()
    (School of Accounting, Economics and Finance, Deakin University, Melbourne, VIC 3125, Australia; Department of Economics, University of Kiel, 24118 Kiel, Germany)

  • T. DI MATTEO

    ()
    (Department of Applied Mathematics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia)

  • THOMAS LUX

    ()
    (Department of Economics, University of Kiel, 24118 Kiel, Germany; Institute for the World Economy, D├╝sternbrooker Weg 120, 24105 Kiel, Germany)

Abstract

In this paper, we consider daily financial data from various sources (stock market indices, foreign exchange rates and bonds) and analyze their multiscaling properties by estimating the parameters of a Markov-switching multifractal (MSM) model with Lognormal volatility components. In order to see how well estimated models capture the temporal dependency of the empirical data, we estimate and compare (generalized) Hurst exponents for both empirical data and simulated MSM models. In general, the Lognormal MSM models generate "apparent" long memory in good agreement with empirical scaling provided that one uses sufficiently many volatility components. In comparison with a Binomial MSM specification [11], results are almost identical. This suggests that a parsimonious discrete specification is flexible enough and the gain from adopting the continuous Lognormal distribution is very limited.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal Advances in Complex Systems.

Volume (Year): 11 (2008)
Issue (Month): 05 ()
Pages: 669-684

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Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:05:p:669-684

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Keywords: Markov-switching multifractal; scaling; Hurst exponent;

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Cited by:
  1. Morales, Raffaello & Di Matteo, T. & Aste, Tomaso, 2013. "Non-stationary multifractality in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6470-6483.
  2. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
  3. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
  4. Raffaello Morales & T. Di Matteo & Ruggero Gramatica & Tomaso Aste, 2011. "Dynamical Hurst exponent as a tool to monitor unstable periods in financial time series," Papers 1109.0465, arXiv.org.

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