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Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation

Author

Listed:
  • Stan Hurn
  • J.Jeisman
  • K.A. Lindsay

    (School of Economics and Finance, Queensland University of Technology)

Abstract

Many stochastic differential equations (SDEs) do not have readily available closed-form expressions for their transitional probability density functions (PDFs). As a result, a large number of competing estimation approaches have been proposed in order to obtain maximum-likelihood estimates of their parameters. Arguably the most straightforward of these is one in which the required estimates of the transitional PDF are obtained by numerical solution of the Fokker-Planck (or forward-Kolmogorov) partial differential equation. Despite the fact that this method produces accurate estimates and is completely generic, it has not proved popular in the applied literature. Perhaps this is attributable to the fact that this approach requires repeated solution of a parabolic partial differential equation to obtain the transitional PDF and is therefore computationally quite expensive. In this paper, three avenues for improving the reliability and speed of this estimation method are introduced and explored in the context of estimating the parameters of the popular Cox-Ingersoll-Ross and Ornstein-Uhlenbeck models. The recommended algorithm that emerges from this investigation is seen to offer substantial gains in reliability and computational time.

Suggested Citation

  • Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation," Stan Hurn Discussion Papers 2006-01, School of Economics and Finance, Queensland University of Technology.
    • Handle: RePEc:qut:sthurn:2006-01
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    File URL: http://www.bus.qut.edu.au/stanhurn/documents/OldDogNewTricks.pdf
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    References listed on IDEAS

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    2. Lux, Thomas, 2009. "Rational forecasts or social opinion dynamics? Identification of interaction effects in a business climate survey," Journal of Economic Behavior & Organization, Elsevier, vol. 72(2), pages 638-655, November.
    3. Thomas Lux & Jaba Ghonghadze, 2011. "Modeling the Dynamics of EU Economic Sentiment Indicators: An Interaction-Based Approach," Post-Print hal-00711445, HAL.
    4. Jaba Ghonghadze & Thomas Lux, 2012. "Modelling the dynamics of EU economic sentiment indicators: an interaction-based approach," Applied Economics, Taylor & Francis Journals, vol. 44(24), pages 3065-3088, August.
    5. Thomas Lux, 2009. "Rational Forecasts or Social Opinion Dynamics? Identification of Interaction Effects in a Business Climate Survey," Post-Print hal-00720175, HAL.
    6. Ghonghadze, Jaba & Lux, Thomas, 2009. "Modeling the dynamics of EU economic sentiment indicators: an interaction-based approach," Kiel Working Papers 1487, Kiel Institute for the World Economy (IfW Kiel).

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    stochastic differential equations; maximum likelihood; finite difference; finite element; cumulative distribution function; interpolation.;
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