IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1332.html
   My bibliography  Save this paper

Fully Nonparametric Estimation of Scalar Diffusion Models

Author

Listed:

Abstract

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter. The asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens (that is, we implement both infill and long span asymptotics). We prove consistency and convergence to mixtures of normal laws, where the mixing variates depend on the chronological local time of the underlying process, that is the time spent by the process in the vicinity of a spatial point. The estimation method and asymptotic results apply to both stationary and nonstationary processes.

Suggested Citation

  • Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1332
    Note: CFP 1050.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d13/d1332.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    3. repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
    4. Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    5. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(3), pages 365-383, December.
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eric Ghysels & Serena Ng, 1998. "A Semiparametric Factor Model Of Interest Rates And Tests Of The Affine Term Structure," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 535-548, November.
    2. Fornari, Fabio & Mele, Antonio, 2001. "Recovering the probability density function of asset prices using garch as diffusion approximations," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 83-110, March.
    3. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    4. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    5. Viviana Fernández, 1999. "Estructura de Tasas de Interés en Chile: La Vía No Paramétrica," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 36(109), pages 1005-1034.
    6. Matthew Pritsker, 1997. "Nonparametric density estimation and tests of continuous time interest rate models," Finance and Economics Discussion Series 1997-26, Board of Governors of the Federal Reserve System (U.S.).
    7. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    8. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    9. Gómez-Valle, Lourdes & Marti­nez-Rodri­guez, Julia, 2008. "Modelling the term structure of interest rates: An efficient nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 32(4), pages 614-623, April.
    10. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    11. repec:wyi:journl:002108 is not listed on IDEAS
    12. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    13. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    14. Tauchen, George, 2001. "Notes on financial econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 57-64, January.
    15. Lee, Myoung-jae & Li, Wen-juan, 2005. "Drift and diffusion function specification for short-term interest rates," Economics Letters, Elsevier, vol. 86(3), pages 339-346, March.
    16. Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Universite de Montreal, Departement de sciences economiques.
    17. Chew Lian Chua & Sandy Suardi, 2005. "Is There a Unit Root in East-Asian Short-Term Interest Rates?," Melbourne Institute Working Paper Series wp2005n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    18. Bali, Turan G. & Neftci, Salih N., 2003. "Disturbing extremal behavior of spot rate dynamics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 455-477, September.
    19. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    20. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
    21. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.

    More about this item

    Keywords

    Diffusion; Drift; Infill asymptotics; Kernel density; Local time; Long span asymptotics; Martingale; Nonparametric estimation; Semimartingale; Stochastic differential equation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cwl:cwldpp:1332. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.