IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/2017.html
   My bibliography  Save this paper

More efficient kernel estimation in nonparametric regression with autocorrelated errors

Author

Listed:
  • Carroll, Raymond J
  • Linton, Oliver
  • Mammen, Enno
  • Xiao, Zhijie

Abstract

We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that has to be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. It is shown that the proposed estimation procedure is more efficient than the conventional kernel method. We also provide simulation evidence to suggest that gains can be achieved in moderate sized samples.

Suggested Citation

  • Carroll, Raymond J & Linton, Oliver & Mammen, Enno & Xiao, Zhijie, 2002. "More efficient kernel estimation in nonparametric regression with autocorrelated errors," LSE Research Online Documents on Economics 2017, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2017
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/2017/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    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. Fan, J. & Härdle, Wolfgang & Mammen, Enno, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    5. 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.
    6. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.
    2. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.

    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. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    3. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    4. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    6. Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 145-174.
    7. Lubrano, Michel, 2004. "Modélisation bayésienne non linéaire du taux d’intérêt de court terme américain : l’aide des outils non paramétriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 465-499, Juin-Sept.
    8. Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Universite de Montreal, Departement de sciences economiques.
    9. Semeyutin, Artur & O’Neill, Robert, 2019. "A brief survey on the choice of parameters for: “Kernel density estimation for time series data”," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    10. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 1998. "Semiparametric additive indices for binary response and generalized additive models," SFB 373 Discussion Papers 1998,95, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Martin D. D. Evans & Richard K. Lyons, 2017. "Time-Varying Liquidity in Foreign Exchange," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 8, pages 325-361, World Scientific Publishing Co. Pte. Ltd..
    12. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    13. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    14. Martin D. D. Evans & Richard K. Lyons, 2017. "Are Different-Currency Assets Imperfect Substitutes?," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 10, pages 415-456, World Scientific Publishing Co. Pte. Ltd..
    15. 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.).
    16. Martin D. D. Evans & Richard K. Lyons, 2001. "Portfolio Balance, Price Impact, and Secret Intervention," NBER Working Papers 8356, National Bureau of Economic Research, Inc.
    17. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    18. Herwartz, Helmut & Reimers, Hans-Eggert, 2006. "Modelling the Fisher hypothesis: World wide evidence," Economics Working Papers 2006-04, Christian-Albrechts-University of Kiel, Department of Economics.
    19. Severance-Lossin, E. & Sperlich, S., 1995. "Estimation of Derivatives for Additive Separable Models," SFB 373 Discussion Papers 1995,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    20. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, University of Gothenburg, Department of Economics.

    More about this item

    Keywords

    Backfitting; efficiency; kernel estimation; time series;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:ehl:lserod:2017. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.