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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

Author

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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, Düsternbrooker 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.

Suggested Citation

  • Ruipeng Liu & T. Di Matteo & Thomas Lux, 2008. "Multifractality And Long-Range Dependence Of Asset Returns: The Scaling Behavior Of The Markov-Switching Multifractal Model With Lognormal Volatility Components," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 669-684.
    • Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:05:n:s0219525908001969
    DOI: 10.1142/S0219525908001969
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    References listed on IDEAS

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    1. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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    1. Buonocore, R.J. & Aste, T. & Di Matteo, T., 2016. "Measuring multiscaling in financial time-series," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 38-47.
    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. 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.
    4. Riccardo Junior Buonocore & Tomaso Aste & Tiziana Di Matteo, 2015. "Measuring multiscaling in financial time-series," Papers 1509.05471, arXiv.org, revised Sep 2015.
    5. 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.
    6. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    7. Kukacka, Jiri & Kristoufek, Ladislav, 2021. "Does parameterization affect the complexity of agent-based models?," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 324-356.
    8. Antoniades, I.P. & Brandi, Giuseppe & Magafas, L. & Di Matteo, T., 2021. "The use of scaling properties to detect relevant changes in financial time series: A new visual warning tool," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    9. Bjoern Schulte-Tillman & Mawuli Segnon & Bernd Wilfling, 2022. "Financial-market volatility prediction with multiplicative Markov-switching MIDAS components," CQE Working Papers 9922, Center for Quantitative Economics (CQE), University of Muenster.
    10. Saâdaoui, Foued, 2018. "Testing for multifractality of Islamic stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 263-273.

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