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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

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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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    1. Gagelmann, Frank & Hansjürgens, Bernd, 2002. "Der neue CO2-Emissionshandel in der EU," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW – German National Library of Economics / Leibniz Information Centre for Economics, vol. 82(4), pages 226-234.
    2. Gersbach, Hans & Requate, Till, 2004. "Emission taxes and optimal refunding schemes," Journal of Public Economics, Elsevier, vol. 88(3-4), pages 713-725, March.
    3. Bohringer, Christoph & Lange, Andreas, 2005. "On the design of optimal grandfathering schemes for emission allowances," European Economic Review, Elsevier, vol. 49(8), pages 2041-2055, November.
    4. Copeland, Brian R & Taylor, M Scott, 1995. "Trade and Transboundary Pollution," American Economic Review, American Economic Association, vol. 85(4), pages 716-737, September.
    5. Unold, Wolfram & Requate, Till, 2001. "Pollution control by options trading," Economics Letters, Elsevier, vol. 73(3), pages 353-358, December.
    6. Spulber, Daniel F., 1985. "Effluent regulation and long-run optimality," Journal of Environmental Economics and Management, Elsevier, vol. 12(2), pages 103-116, June.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.

    More about this item

    Keywords

    Markov-switching multifractal; scaling; return volatility;

    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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