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Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey

Author

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  • Helle Sørensen

    (Institute of Economics, University of Copenhagen)

Abstract

This paper is a survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating functions; (ii) analytical and numerical approximations of the likelihood which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation.

Suggested Citation

  • Helle Sørensen, 2002. "Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey," Discussion Papers 02-08, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:0208
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2002/0208.pdf/
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    3. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    6. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    7. Mathieu Kessler, 2000. "Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 65-82, March.
    8. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    9. Mathieu Kessler & Silvestre Paredes, 2002. "Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 425-440, September.
    10. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    11. 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.
    12. Martin Jacobsen, 2001. "Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ‐optimality," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 123-149, March.
    13. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
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    Cited by:

    1. Cysne, Rubens Penha, 2004. "On the Statistical Estimation of Diffusion Processes: A Partial Survey," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    2. Cysne, Rubens Penha, 2004. "On the statistical estimation of diffusion processes: a survey," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 540, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).

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    More about this item

    Keywords

    Bayesian analysis; diffusion processes; discrete-time observations; efficient method of moments (EMM); estimating functions; indirect inference; likelihood approximations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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