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Simulation of multivariate diffusion bridges

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  • Mogens Bladt
  • Samuel Finch
  • Michael Sørensen

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.
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  • Mogens Bladt & Samuel Finch & Michael Sørensen, 2016. "Simulation of multivariate diffusion bridges," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 343-369, March.
    • Handle: RePEc:bla:jorssb:v:78:y:2016:i:2:p:343-369
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    File URL: http://hdl.handle.net/10.1111/rssb.12118
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    1. 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.
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    8. 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.
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    Cited by:

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    3. Valerie Girardin & Rachid Senoussi, 2020. "Filling the gap between Continuous and Discrete Time Dynamics of Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 590-602, July.

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    More about this item

    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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