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Truncated dynamics and estimation of diffusion equations

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  • Darolles, Serge
  • Gourieroux, Christian

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

  • Darolles, Serge & Gourieroux, Christian, 2001. "Truncated dynamics and estimation of diffusion equations," Journal of Econometrics, Elsevier, vol. 102(1), pages 1-22, May.
    • Handle: RePEc:eee:econom:v:102:y:2001:i:1:p:1-22
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    References listed on IDEAS

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    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    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. Serge Darolles & Jean-Pierre Florens & Christian Gourieroux, 1998. "Kernel Based Nonlinear Canonical Analysis," Working Papers 98-55, Center for Research in Economics and Statistics.
    4. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    5. repec:crs:wpaper:9855 is not listed on IDEAS
    6. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    7. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    8. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
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    Citations

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    Cited by:

    1. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, Department of Economics and Business Economics, Aarhus University.
    2. 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.
    3. Bernd Wilfling, 2003. "Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch Regimes," German Economic Review, Verein für Socialpolitik, vol. 4, pages 433-457, November.
    4. Bernd Wilfling, 2003. "Interest Rate Volatility Prior to Monetary Union under Alternative Pre‐Switch Regimes," German Economic Review, Verein für Socialpolitik, vol. 4(4), pages 433-457, November.
    5. 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.
    6. Christian Gouriéroux & Eric Renault & Pascale Valery, 2007. "Diffusion Processes with Polynomial Eigenfunctions," Annals of Economics and Statistics, GENES, issue 85, pages 115-130.
    7. 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.
    8. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    9. 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.
    10. 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.
    11. repec:adr:anecst:y:2007:i:85:p:05 is not listed on IDEAS
    12. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    13. 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.

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