Estimation of Diffusion Parameters by a Nonparametric Drift Function Model

  • Isao Shoji
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2690)


The paper presents a method to estimate diffusion parameters without specifying drift functions of one dimensional stochastic differential equations. We study finite sample properties of the estimator by numerical experiments at several observation time intervals with total time interval fixed. The results show the estimator is getting efficient as observation time interval becomes smaller. By comparing with the quadratic variation method which is proven to have consistency, the proposed method produces almost the same finite sample properties as that.


Observation Time Interval Discretized Process Drift Function Discrete Time Series Total Time Interval 
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  1. 1.
    Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice- Hall, New Jersey (1979)zbMATHGoogle Scholar
  2. 2.
    Chen, R., Tsay, R.S.: Functional-coefficient autoregressive models. J. Am. Statist. Assoc. 88, 298–308 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cheng, M., Hall, P., Turlach, B.A.: High-derivative parametric enhancements of nonparametric curve estimation. Biometrika 86, 417–428 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fan, J., Gijbels, I.: Local Polynomial Modelling and Its Applications. Chapman and Hall, London (1996)zbMATHGoogle Scholar
  5. 5.
    Fan, J., Hall, P., Martin, M.A., Patil, P.: On local smoothing of nonparametric curve estimators. J. Am. Statist. Assoc. 91, 258–266 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Florens-Zmirou, D.: Approximate discrete-time schemes for statistics of diffusion processes. Statistics 20, 547–557 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Linton, O.B.: Efficient estimation of additive nonparametric regression models. Biometrika 84, 469–473 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Linton, O.B., Chen, R., Wang, N., Härdle, W.: An analysis of transformations for additive nonparametric regression. J. Am. Statist. Assoc. 92, 1512–1521 (1997)zbMATHCrossRefGoogle Scholar
  9. 9.
    Shoji, I.: Nonparametric state estimation of diffusion processes. Biometrika 89, 451–456 (1998)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Shoji, I., Ozaki, T.: A statistical method of estimation and simulation for systems of stochastic differential equations. Biometrika 85, 240–243 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Tjøsthaim, D., Auestad, B.H.: Nonparametric identification of nonlinear time series: projections. J. Am. Statist. Assoc. 89, 258–266 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Isao Shoji
    • 1
  1. 1.Institute of Policy and Planning SciencesUniversity of TsukubaTsukuba IbarakiJapan

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