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A new technique for simulating the likelihood of stochastic differential equations

Author

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  • João Nicolau

    (Universidade Técnica de Lisboa, Instituto Superior de Economia e Gestão, Portugal)

Abstract

This article presents a new simulation-based technique for estimating the likelihood of stochastic differential equations. This technique is based on a result of Dacunha-Castelle and Florens-Zmirou. These authors proved that the transition densities of a nonlinear diffusion process with a constant diffusion coefficient can be written in a closed form involving a stochastic integral. We show that this stochastic integral can be easily estimated through simulations and we prove a convergence result. This simulator for the transition density is used to obtain the simulated maximum likelihood (SML) estimator. We show through some Monte Carlo experiments that our technique is highly computationally efficient and the SML estimator converges rapidly to the maximum likelihood estimator. Copyright Royal Economic Society 2002

Suggested Citation

  • João Nicolau, 2002. "A new technique for simulating the likelihood of stochastic differential equations," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 91-103, June.
    • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:1:p:91-103
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    References listed on IDEAS

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    10. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
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    Cited by:

    1. Siddhartha Chib & Michael K Pitt & Neil Shephard, 2004. "Likelihood based inference for diffusion driven models," OFRC Working Papers Series 2004fe17, Oxford Financial Research Centre.
    2. Stefano Maria IACUS & Alessandro DE GREGORIO, 2010. "Adaptive LASSO-type estimation for ergodic diffusion processes," Departmental Working Papers 2010-13, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Umberto Picchini & Andrea De Gaetano & Susanne Ditlevsen, 2010. "Stochastic Differential Mixed‐Effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 67-90, March.
    4. Nicolau João, 2011. "Purchasing Power Parity Analyzed from a Continuous-Time Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-26, May.
    5. Nicolau, João, 2011. "Purchasing Power Parity analyzed through a continuous-time version of the ESTAR model," Economics Letters, Elsevier, vol. 110(3), pages 182-185, March.
    6. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 24, July-Dece.
    7. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2004.
    8. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    9. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777, September.
    10. Møller, Jan Kloppenborg & Madsen, Henrik & Carstensen, Jacob, 2011. "Parameter estimation in a simple stochastic differential equation for phytoplankton modelling," Ecological Modelling, Elsevier, vol. 222(11), pages 1793-1799.

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