IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v47y2006i1p1-15.html
   My bibliography  Save this article

Kernel smoothed prediction intervals for ARMA models

Author

Listed:
  • Klaus Abberger

Abstract

The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this paper we apply nonparametric quantile regression to the empirical forecast errors using lead time as regressor. With this method there is no need for a distribution assumption. But for the data pattern in this case a double kernel method which allows smoothing in two directions is required. An estimation algorithm is presented and applied to some simulation examples.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Klaus Abberger, 2006. "Kernel smoothed prediction intervals for ARMA models," Statistical Papers, Springer, vol. 47(1), pages 1-15, January.
    • Handle: RePEc:spr:stpapr:v:47:y:2006:i:1:p:1-15
    DOI: 10.1007/s00362-005-0269-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-005-0269-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-005-0269-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    2. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    3. Tsay, Ruey S, 1993. "Calculating Interval Forecasts: Comment: Adaptive Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 140-142, April.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. Roberto Buizza & James W. Taylor, 2004. "A comparison of temperature density forecasts from GARCH and atmospheric models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(5), pages 337-355.
    2. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    3. Kim, Jae H. & Wong, Kevin & Athanasopoulos, George & Liu, Shen, 2011. "Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals," International Journal of Forecasting, Elsevier, vol. 27(3), pages 887-901, July.
    4. Phathutshedzo Mpfumali & Caston Sigauke & Alphonce Bere & Sophie Mulaudzi, 2019. "Day Ahead Hourly Global Horizontal Irradiance Forecasting—Application to South African Data," Energies, MDPI, vol. 12(18), pages 1-28, September.
    5. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    6. Taylor, James W., 2007. "Forecasting daily supermarket sales using exponentially weighted quantile regression," European Journal of Operational Research, Elsevier, vol. 178(1), pages 154-167, April.
    7. Ly, Sel & Xie, Jiahang & Wolter, Franz-Erich & Nguyen, Hung D. & Weng, Yu, 2023. "T-shape data and probabilistic remaining useful life prediction for Li-ion batteries using multiple non-crossing quantile long short-term memory," Applied Energy, Elsevier, vol. 349(C).
    8. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    9. He, Yaoyao & Liu, Rui & Li, Haiyan & Wang, Shuo & Lu, Xiaofen, 2017. "Short-term power load probability density forecasting method using kernel-based support vector quantile regression and Copula theory," Applied Energy, Elsevier, vol. 185(P1), pages 254-266.
    10. Berrin Aytac & S. Wu, 2013. "Characterization of demand for short life-cycle technology products," Annals of Operations Research, Springer, vol. 203(1), pages 255-277, March.
    11. Lee, Yun Shin & Scholtes, Stefan, 2014. "Empirical prediction intervals revisited," International Journal of Forecasting, Elsevier, vol. 30(2), pages 217-234.
    12. repec:lan:wpaper:470 is not listed on IDEAS
    13. Charles, Amelie & Darne, Olivier & Kim, Jae, 2016. "Stock Return Predictability: Evaluation based on Prediction Intervals," MPRA Paper 70143, University Library of Munich, Germany.
    14. Dhaoui, Iyad, 2015. "Climat des Affaires et Compétitivité de l’Entreprise Tunisienne Après la Révolution : Analyses et Perspectives [Business Climate and Competitiveness of the Tunisian Enterprise After the Revolution:," MPRA Paper 87331, University Library of Munich, Germany.
    15. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2005. "Bootstrap prediction intervals for power-transformed time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 219-235.
    16. Li, Yushu & Andersson, Jonas, 2014. "A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting," Discussion Papers 2014/12, Norwegian School of Economics, Department of Business and Management Science.
    17. Yushu Li & Jonas Andersson, 2020. "A likelihood ratio and Markov chain‐based method to evaluate density forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 47-55, January.
    18. James W. Taylor & Derek W. Bunn, 1999. "A Quantile Regression Approach to Generating Prediction Intervals," Management Science, INFORMS, vol. 45(2), pages 225-237, February.
    19. Wolfgang Nierhaus, 2019. "Business Cycle 2018: Forecast and Reality," ifo Schnelldienst, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 72(03), pages 22-29, February.
    20. Melard, G. & Pasteels, J. -M., 2000. "Automatic ARIMA modeling including interventions, using time series expert software," International Journal of Forecasting, Elsevier, vol. 16(4), pages 497-508.
    21. Harvey, David I. & Newbold, Paul, 2003. "The non-normality of some macroeconomic forecast errors," International Journal of Forecasting, Elsevier, vol. 19(4), pages 635-653.

    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:spr:stpapr:v:47:y:2006:i:1:p:1-15. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.