IDEAS home Printed from https://ideas.repec.org/p/cdl/ucsdec/qt67h5s74t.html
   My bibliography  Save this paper

Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions

Author

Listed:
  • Pan, Li
  • Politis, Dimitris N

Abstract

In order to construct prediction intervals without the combersome--and typically unjustifiable--assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studies in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the constructuion of bootstrap prediction intervals. Forward and backward bootstrap methods for using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as essimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their acheived coverage level and length of interval.Â

Suggested Citation

  • Pan, Li & Politis, Dimitris N, 2014. "Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions," University of California at San Diego, Economics Working Paper Series qt67h5s74t, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt67h5s74t
    as

    Download full text from publisher

    File URL: http://www.escholarship.org/uc/item/67h5s74t.pdf;origin=repeccitec
    Download Restriction: no

    References listed on IDEAS

    as
    1. Jesús Miguel & Pilar Olave, 1999. "Bootstrapping forecast intervals in ARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 345-364, December.
    2. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    3. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    4. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    5. Pilar Olave Robio, 1999. "Forecast intervals in ARCH models: bootstrap versus parametric methods," Applied Economics Letters, Taylor & Francis Journals, vol. 6(5), pages 323-327.
    6. Dimitris Politis, 2013. "Rejoinder on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 240-250, June.
    7. Olive, David J., 2007. "Prediction intervals for regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3115-3122, March.
    8. Arup Bose & Kanchan Mukherjee, 2003. "Estimating The Arch Parameters By Solving Linear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 127-136, March.
    9. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
    10. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    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. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Michael Wolf & Dan Wunderli, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 352-376, May.
    2. Sílvia Gonçalves & Benoit Perron & Antoine Djogbenou, 2016. "Bootstrap prediction intervals for factor models," CIRANO Working Papers 2016s-19, CIRANO.

    More about this item

    Keywords

    Physical Sciences and Mathematics; Confidence intervals; forecasting; time series;

    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:cdl:ucsdec:qt67h5s74t. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lisa Schiff). General contact details of provider: http://edirc.repec.org/data/deucsus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.