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Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes

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  • Arenas, Zochil González
  • Jimenez, Juan Carlos
  • Lozada-Chang, Li-Vang
  • Santana, Roberto

Abstract

Innovation Method is a recognized method for the estimation of parameters in diffusion processes. It is well known that the quality of the Innovation Estimator strongly depends on an adequate selection of the initial value for the parameters when a local optimization algorithm is used in its computation. Alternatively, in this paper, we use a strategy based on a modern method for solving global optimization problems, Estimation of Distribution Algorithms (EDAs). We study the feasibility of a specific EDA - a continuous version of the Univariate Marginal Distribution Algorithm (UMDAc) - for the computation of the Innovation Estimators. Through numerical simulations, we show that the considered global optimization algorithms substantially improves the effectiveness of the Innovation Estimators for different types of diffusion processes with complex nonlinear and stochastic dynamics.

Suggested Citation

  • Arenas, Zochil González & Jimenez, Juan Carlos & Lozada-Chang, Li-Vang & Santana, Roberto, 2021. "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 449-467.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:449-467
    DOI: 10.1016/j.matcom.2021.03.017
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    References listed on IDEAS

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    1. Jan Nygaard Nielsen & Martin Vestergaard, 2000. "Estimation In Continuous-Time Stochastic Volatility Models Using Nonlinear Filters," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 279-308.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Bosman, Peter A.N. & Grahl, Jorn, 2008. "Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1246-1264, March.
    5. T. Ozaki & J. C. Jimenez & V. Haggan‐Ozaki, 2000. "The Role of the Likelihood Function in the Estimation of Chaos Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 363-387, July.
    6. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    7. Jan Nygaard Nielsen & Martin Vestergaard, 2000. "Erratum: "Estimation In Continuous-Time Stochastic Volatility Models Using Nonlinear Filters"," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 731-731.
    8. J. C. Jimenez & T. Ozaki, 2006. "An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 77-97, January.
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