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Maximum likelihood estimation for integrated diffusion processes


  • Fernando Baltazar-Larios

    () (Universidad Nacional Autónoma de México)

  • Michael Sørensen

    () (University of Copenhagen and CREATES)


We propose a method for obtaining maximum likelihood estimates of parameters in diffusion models when the data is a discrete time sample of the integral of the process, while no direct observations of the process itself are available. The data are, moreover, assumed to be contaminated by measurement errors. Integrated volatility is an example of this type of observations. Another example is ice-core data on oxygen isotopes used to investigate paleo-temperatures. The data can be viewed as incomplete observations of a model with a tractable likelihood function. Therefore we propose a simulated EM-algorithm to obtain maximum likelihood estimates of the parameters in the diffusion model. As part of the algorithm, we use a recent simple method for approximate simulation of diffusion bridges. In simulation studies for the Ornstein-Uhlenbeck process and the CIR process the proposed method works well.

Suggested Citation

  • Fernando Baltazar-Larios & Michael Sørensen, 2010. "Maximum likelihood estimation for integrated diffusion processes," CREATES Research Papers 2010-33, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-33

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    References listed on IDEAS

    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Manuel S. Santos, 2006. "Convergence Properties of the Likelihood of Computed Dynamic Models," Econometrica, Econometric Society, vol. 74(1), pages 93-119, January.
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    More about this item


    Diffusion bridge; discretely sampled diffusions; EM-algorithm; likelihood inference; measurement error; stochastic differential equation; stochastic volatility.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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