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A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions


  • Stan Hurn

    () (QUT)

  • Andrew McClelland

    () (QUT)

  • Kenneth Lindsay

    () (University of Glasgow)


This paper develops a quasi-maximum likelihood (QML) procedure for estimating the parameters of multi-dimensional stochastic differential equations. The transitional density is taken to be a time-varying multivariate Gaussian where the first two moments of the distribution are approximately the true moments of the unknown transitional density. For affine drift and diffusion functions, the moments are shown to be exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good. The estimation procedure is easily generalizable to models with latent factors, such as the stochastic volatility class of model. The QML method is as effective as alternative methods when proxy variables are used for unobserved states. A conditioning estimation procedure is also developed that allows parameter estimation in the absence of proxies.

Suggested Citation

  • Stan Hurn & Andrew McClelland & Kenneth Lindsay, 2010. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," NCER Working Paper Series 65, National Centre for Econometric Research.
  • Handle: RePEc:qut:auncer:2010_12

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    Cited by:

    1. Matyas Barczy & Balazs Nyul & Gyula Pap, 2015. "Least squares estimation for the subcritical Heston model based on continuous time observations," Papers 1511.05948,, revised Nov 2017.
    2. esposito, francesco paolo & cummins, mark, 2015. "Filtering and likelihood estimation of latent factor jump-diffusions with an application to stochastic volatility models," MPRA Paper 64987, University Library of Munich, Germany.
    3. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.
    4. Matyas Barczy & Gyula Pap & Tamas T. Szabo, 2014. "Parameter estimation for the subcritical Heston model based on discrete time observations," Papers 1403.0527,, revised Feb 2016.

    More about this item


    stochastic differential equations; parameter estimation; quasi-maximum likelihood; moments;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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