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

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Author Info
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.

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Publisher Info
Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 02-08.

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Length: 19 pages
Date of creation: Aug 2002
Date of revision:
Handle: RePEc:kud:kuiedp:0208

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Related research
Keywords: Bayesian analysis; diffusion processes; discrete-time observations; efficient method of moments (EMM); estimating functions; indirect inference; likelihood approximations;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jean Jacod, 2000. "Non-parametric Kernel Estimation of the Coefficient of a Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 27(1), pages 83-96. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08. [Downloadable!] (restricted)
  4. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April. [Downloadable!] (restricted)
  5. Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series 2000mf02, Oxford Financial Research Centre. [Downloadable!]
    Other versions:
  6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  7. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
    Other versions:
  8. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De. [Downloadable!] (restricted)
    Other versions:
  9. Helle Sørensen, 2003. "Simulated Likelihood Approximations for Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 30(2), pages 257-276. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
    Other versions:
  11. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  12. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  13. Bo Martin Bibby, 2001. "Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 28(1), pages 99-112. [Downloadable!] (restricted)
  14. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  15. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
  16. 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. [Downloadable!] (restricted)
  17. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 10(3), pages 525-77.
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