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A multifractal approach towards inference in finance

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  • Ola L{\o}vsletten
  • Martin Rypdal
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    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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    File URL: http://arxiv.org/pdf/1202.5376
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1202.5376.

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    Date of creation: Feb 2012
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    Handle: RePEc:arx:papers:1202.5376

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    Web page: http://arxiv.org/

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    1. Hans J. Skaug & Jun Yu, 2009. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 15-2009, Singapore Management University, School of Economics.
    2. A. Ian McLeod & Hao Yu & Zinovi L. Krougly, . "Algorithms for Linear Time Series Analysis: With R Package," Journal of Statistical Software, American Statistical Association, vol. 23(i05).
    3. Laurent Calvet & Adlai Fisher, 1999. "Forecasting Multifractal Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-017, New York University, Leonard N. Stern School of Business-.
    4. Sara Martino & Kjersti Aas & Ola Lindqvist & Linda Neef & H�vard 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.
    5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    6. Thomas Lux, 2006. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Working Papers wp06-19, Warwick Business School, Finance Group.
    7. Ravi Varadhan & Paul Gilbert, . "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, American Statistical Association, vol. 32(i04).
    8. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
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