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Simulation of multivariate diffusion bridges

Author

Listed:
  • Mogens Bladt

    (Universidad Nacional Autónoma de México)

  • Samuel Finch

    (University of Copenhagen, Dept. of Mathematical Sciences)

  • Michael Sørensen

    (University of Copenhagen, Dept. of Mathematical Sciences and CREATES)

Abstract

We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes a previously proposed simulation method for one-dimensional bridges to the multi-variate setting. First a method of simulating approximate, but often very accurate, diffusion bridges is proposed. These approximate bridges are used as proposal for easily implementable MCMC algorithms that produce exact diffusion bridges. The new method is much more generally applicable than previous methods. Another advantage is that the new method works well for diffusion bridges in long intervals because the computational complexity of the method is linear in the length of the interval. In a simulation study the new method performs well, and its usefulness is illustrated by an application to Bayesian estimation for the multivariate hyperbolic diffusion model.

Suggested Citation

  • Mogens Bladt & Samuel Finch & Michael Sørensen, 2014. "Simulation of multivariate diffusion bridges," CREATES Research Papers 2014-16, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-16
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    References listed on IDEAS

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    1. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    2. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    3. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382, June.
    4. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    5. Lin, Ming & Chen, Rong & Mykland, Per, 2010. "On Generating Monte Carlo Samples of Continuous Diffusion Bridges," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 820-838.
    6. Delyon, Bernard & Hu, Ying, 2006. "Simulation of conditioned diffusion and application to parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1660-1675, November.
    7. Golightly, A. & Wilkinson, D.J., 2008. "Bayesian inference for nonlinear multivariate diffusion models observed with error," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1674-1693, January.
    8. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    9. A. Golightly & D. J. Wilkinson, 2005. "Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation," Biometrics, The International Biometric Society, vol. 61(3), pages 781-788, September.
    10. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-191, April.
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    Cited by:

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    3. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.

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    More about this item

    Keywords

    Bayesian inference; coupling; discretely sampled diffusions; likelihood inference; stochastic differential equation; time-reversal.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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