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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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  • Ruipeng Liu
  • Tiziana Di Matteo
  • Thomas Lux

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

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Bibliographic Info

Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1427.

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Length: 15 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:kie:kieliw:1427

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Keywords: Markov-switching multifractal; scaling; return volatility;

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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. 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. Jozef Barunik & Tomaso Aste & Tiziana Di Matteo & Ruipeng Liu, 2012. "Understanding the source of multifractality in financial markets," Papers 1201.1535, arXiv.org, revised Jan 2012.
  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.

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