IDEAS home Printed from https://ideas.repec.org/p/uts/ppaper/1996-2.html
   My bibliography  Save this paper

On effects of discretization on estimators of drift parameters for diffusion processes

Author

Abstract

In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

Suggested Citation

  • P. E. Kloeden & Eckhard Platen & H. Schurz & M. Sørensen, 1996. "On effects of discretization on estimators of drift parameters for diffusion processes," Published Paper Series 1996-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:1996-2
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-effects-of-discretization-on-estimators-of-drift-parameters-for-diffusion-processes/2EE909A5CBA70C20B80119E36AF081B0
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. C. H. Skiadas & A. N. Giovanis, 1997. "A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(2), pages 85-101, June.
    2. Óscar Cornejo & Sebastián Muñoz-Herrera & Felipe Baesler & Rodrigo Rebolledo, 2023. "The Application of the Random Time Transformation Method to Estimate Richards Model for Tree Growth Prediction," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    3. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    4. Kim, Myung Suk & Wang, Suojin, 2006. "Sizes of two bootstrap-based nonparametric specification tests for the drift function in continuous time models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1793-1806, April.
    5. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
    6. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
    7. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.
    8. Cleur, Eugene M & Manfredi, Piero, 1999. "One Dimensional SDE Models, Low Order Numerical Methods and Simulation Based Estimation: A Comparison of Alternative Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 13(2), pages 177-197, April.
    9. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    10. Martin J. Lenardon & Anna Amirdjanova, 2006. "Interaction between stock indices via changepoint analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(5‐6), pages 573-586, September.
    11. Kim, Myung Suk & Wang, Suojin, 2008. "Consistent estimation in regression models for the drift function in some continuous time models," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2682-2691, January.
    12. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, January.
    13. Yvo Pokern & Andrew M. Stuart & Petter Wiberg, 2009. "Parameter estimation for partially observed hypoelliptic diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 49-73, January.
    14. Suk Kim, Myung & Wang, Suojin, 2006. "On the applicability of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2210-2217, December.
    15. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
    16. 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.
    17. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, January.
    18. João Nicolau, 2002. "A new technique for simulating the likelihood of stochastic differential equations," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 91-103, June.
    19. Fan, Jianqing & Fan, Yingying & Jiang, Jiancheng, 2007. "Dynamic Integration of Time- and State-Domain Methods for Volatility Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 618-631, June.
    20. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:ppaper:1996-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/sfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.