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A multifractal approach towards inference in finance

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  • Ola L{o}vsletten
  • Martin Rypdal

Abstract

We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional densities for one- and multi-step returns. The inference techniques presented in this paper, including maximum likelihood estimation, are applied to data from the Oslo Stock Exchange, and it is observed that the volatility forecasts based on the multifractal random walk have a much richer structure than the forecasts obtained from a basic stochastic volatility model.

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  • Ola L{o}vsletten & Martin Rypdal, 2012. "A multifractal approach towards inference in finance," Papers 1202.5376, arXiv.org.
    • Handle: RePEc:arx:papers:1202.5376
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    References listed on IDEAS

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    1. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
    2. Jun Yu, 2007. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 01-2007, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    3. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    4. McLeod, A. Ian & Yu, Hao & Krougly, Zinovi L., 2007. "Algorithms for Linear Time Series Analysis: With R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i05).
    5. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    6. Sara Martino & Kjersti Aas & Ola Lindqvist & Linda Neef & Håvard Rue, 2011. "Estimating stochastic volatility models using integrated nested Laplace approximations," The European Journal of Finance, Taylor & Francis Journals, vol. 17(7), pages 487-503.
    7. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    8. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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