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More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

Author

Listed:
  • Zhijie Xiao

    (Univ. Illinois, Urbana-Champaign)

  • Oliver Linton

    (LSE)

  • Raymond J. Carroll

    (Texas A&M Univ.)

  • E. Mammen

    (Universitat Heidelberg)

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

  • Zhijie Xiao & Oliver Linton & Raymond J. Carroll & E. Mammen, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," Cowles Foundation Discussion Papers 1375, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1375
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    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. 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.
    3. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    4. 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.
    5. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    6. 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.
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    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.

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    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

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