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Prediction-based estimating functions: review and new developments


  • Michael Sørensen

    () (University of Copenhagen and CREATES)


The general theory of prediction-based estimating functions for stochastic process models is reviewed and extended. Particular attention is given to optimal estimation, asymptotic theory and Gaussian processes. Several examples of applications are presented. In particular partial observation of a systems of stochastic differential equations is discussed. This includes diffusions observed with measurement errors, integrated diffusions, stochastic volatility models, and hypoelliptic stochastic differential equations. The Pearson diffusions, for which explicit optimal prediction-based estimating functions can be found, are briefly presented.

Suggested Citation

  • Michael Sørensen, 2011. "Prediction-based estimating functions: review and new developments," CREATES Research Papers 2011-05, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-05

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    References listed on IDEAS

    1. Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre.
    2. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
    3. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(01), pages 60-93, February.
    4. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278.
    5. Dette, Holger & Podolskij, Mark, 2005. "Testing the parametric form of the volatility in continuous time diffusion models: an empirical process approach," Technical Reports 2005,50, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Asger Lunde & Anne Floor Brix, 2013. "Estimating Stochastic Volatility Models using Prediction-based Estimating Functions," CREATES Research Papers 2013-23, Department of Economics and Business Economics, Aarhus University.
    2. Anne Brix & Asger Lunde, 2015. "Prediction-based estimating functions for stochastic volatility models with noisy data: comparison with a GMM alternative," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 433-465, October.

    More about this item


    Aasymptotic normality; consistency; diffusion with measurement errors; Gaussian process; integrated diffusion; linear predictors; non-Markovian models; optimal estimating function; partially observed system; Pearson diffusion.;

    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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