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Truncated Dynamics and Estimation of DiffusionEquations

Author

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  • Serge Darolles

    (Crest)

  • Christian Gourieroux

    (Crest)

Abstract

We study inference on continuous-time processes from discrete data with a given time interval between consecutive observations, and propose a modification of the sieve estimation method based on the infinitesimal generator. Our approach consists on truncating the initial process to improve the estimation of the eigenfunctions at the boundaries of the set of admissible values. For diffusion processes, nonparametric estimation of the drift and volatility are derived. A prior truncation is also useful to eliminate in practice the specific dynamics of extreme risks.
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Suggested Citation

  • Serge Darolles & Christian Gourieroux, 1997. "Truncated Dynamics and Estimation of DiffusionEquations," Working Papers 97-36, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:97-36
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    Cited by:

    1. is not listed on IDEAS
    2. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, Department of Economics and Business Economics, Aarhus University.
    3. Wilfling Bernd, 2003. "Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch Regimes," German Economic Review, De Gruyter, vol. 4(4), pages 433-457, December.
    4. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    5. repec:bla:germec:v:4:y:2003:i::p:433-457 is not listed on IDEAS
    6. Christian Gourieroux & Hung T. Nguyen & Songsak Sriboonchitta, 2017. "Nonparametric estimation of a scalar diffusion model from discrete time data: a survey," Annals of Operations Research, Springer, vol. 256(2), pages 203-219, September.
    7. Ruijun Bu & Jihyun Kim & Bin Wang, 2020. "Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models," Working Papers 202021, University of Liverpool, Department of Economics.
    8. repec:adr:anecst:y:2007:i:85:p:05 is not listed on IDEAS
    9. Mark Trede & Bernd Wilfling, 2007. "Estimating exchange rate dynamics with diffusion processes: an application to Greek EMU data," Empirical Economics, Springer, vol. 33(1), pages 23-39, July.
    10. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    11. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    12. Christian Gouriéroux & Eric Renault & Pascale Valery, 2007. "Diffusion Processes with Polynomial Eigenfunctions," Annals of Economics and Statistics, GENES, issue 85, pages 115-130.
    13. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.
    14. Dennis Kristensen, 2004. "Estimation in Two Classes of Semiparametric Diffusion Models," FMG Discussion Papers dp500, Financial Markets Group.

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