IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v25y2004i4p449-465.html
   My bibliography  Save this article

Bootstrap predictive inference for ARIMA processes

Author

Listed:
  • Lorenzo Pascual
  • Juan Romo
  • Esther Ruiz

Abstract

. In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving‐average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite‐sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving‐average components.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:449-465
    DOI: 10.1111/j.1467-9892.2004.01713.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2004.01713.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2004.01713.x?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Matteo Grigoletto, 1998. "Bootstrap prediction intervals for autoregressive models fitted to non-autoregressive processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(3), pages 285-295, December.
    2. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2001. "Effects of parameter estimation on prediction densities: a bootstrap approach," International Journal of Forecasting, Elsevier, vol. 17(1), pages 83-103.
    3. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    4. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    5. Jens‐Peter Kreiss & Jürgen Franke, 1992. "Bootstrapping Stationary Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 297-317, July.
    6. 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)

    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. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
    2. Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    4. Kim, Jae H., 2004. "Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators," International Journal of Forecasting, Elsevier, vol. 20(1), pages 85-97.
    5. Chan, W.S & Cheung, S.H & Wu, K.H, 2004. "Multiple forecasts with autoregressive time series models: case studies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 421-430.
    6. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    7. Felix Wick & Ulrich Kerzel & Martin Hahn & Moritz Wolf & Trapti Singhal & Daniel Stemmer & Jakob Ernst & Michael Feindt, 2021. "Demand Forecasting of Individual Probability Density Functions with Machine Learning," SN Operations Research Forum, Springer, vol. 2(3), pages 1-39, September.
    8. Clements, Michael P. & Kim, Jae H., 2007. "Bootstrap prediction intervals for autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3580-3594, April.
    9. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
    10. 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.
    11. Ahmed, Wajid Shakeel & Sheikh, Jibran & Ur-Rehman, Kashif & Shafi, khuram & Shad, Shafqat Ali & Butt, Faisal Shafique, 2020. "New continuum of stochastic static forecasting model for mutual funds at investment policy level," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    12. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    13. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    14. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    15. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    16. repec:cte:wsrepe:ws011409 is not listed on IDEAS
    17. repec:cte:wsrepe:9858 is not listed on IDEAS
    18. Andrés Alonso & Daniel Peña & Juan Romo, 2006. "Introducing model uncertainty by moving blocks bootstrap," Statistical Papers, Springer, vol. 47(2), pages 167-179, March.
    19. Jing Li, 2021. "Block bootstrap prediction intervals for parsimonious first‐order vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 512-527, April.
    20. F. Jay Breidt & Richard A. Davis & William T. M. Dunsmuir, 1995. "Improved Bootstrap Prediction Intervals For Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 177-200, March.
    21. Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    22. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.

    More about this item

    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:bla:jtsera:v:25:y:2004:i:4:p:449-465. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.