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Multifractality and long-range dependence of asset returns: The scaling behaviour of the Markov-switching multifractal model with lognormal volatility components

Author

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  • Liu, Ruipeng
  • Di Matteo, Tiziana
  • Lux, Thomas

Abstract

In this paper we consider daily financial data from various sources (stock market indices, foreign exchange rates and bonds) and analyze their multi-scaling properties by estimating the parameters of a Markov-switching multifractal model (MSM) 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 one uses sufficiently many volatility components. In comparison with a Binomial MSM specification [7], 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

  • Liu, Ruipeng & Di Matteo, Tiziana & Lux, Thomas, 2008. "Multifractality and long-range dependence of asset returns: The scaling behaviour of the Markov-switching multifractal model with lognormal volatility components," Economics Working Papers 2008-09, Christian-Albrechts-University of Kiel, Department of Economics.
    • Handle: RePEc:zbw:cauewp:7371
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    Cited by:

    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. Riccardo Junior Buonocore & Tomaso Aste & Tiziana Di Matteo, 2015. "Measuring multiscaling in financial time-series," Papers 1509.05471, arXiv.org, revised Sep 2015.
    4. 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.
    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. 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.
    9. Liu, Ruipeng & Lux, Thomas, 2010. "Flexible and robust modelling of volatility comovements: a comparison of two multifractal models," Kiel Working Papers 1594, Kiel Institute for the World Economy (IfW Kiel).
    10. 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.
    11. Ioannis P. Antoniades & Giuseppe Brandi & L. G. Magafas & T. Di Matteo, 2020. "The use of scaling properties to detect relevant changes in financial time series: a new visual warning tool," Papers 2010.08890, arXiv.org, revised Dec 2020.
    12. 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).
    13. Saâdaoui, Foued, 2018. "Testing for multifractality of Islamic stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 263-273.

    More about this item

    Keywords

    Markov-switching multifractal; scaling; return volatility;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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