IDEAS home Printed from https://ideas.repec.org/a/bla/jecsur/v24y2010i3p389-401.html
   My bibliography  Save this article

A Unifying View On Multi‐Step Forecasting Using An Autoregression

Author

Listed:
  • Philip Hans Franses
  • Rianne Legerstee

Abstract

This paper unifies two methodologies for multi‐step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short‐horizon forecasts to compute longer‐horizon forecasts, while the estimation method minimizes one‐step‐ahead forecast errors. The second methodology considers direct multi‐step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.

Suggested Citation

  • Philip Hans Franses & Rianne Legerstee, 2010. "A Unifying View On Multi‐Step Forecasting Using An Autoregression," Journal of Economic Surveys, Wiley Blackwell, vol. 24(3), pages 389-401, July.
    • Handle: RePEc:bla:jecsur:v:24:y:2010:i:3:p:389-401
    DOI: 10.1111/j.1467-6419.2009.00581.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-6419.2009.00581.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-6419.2009.00581.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
    ---><---

    References listed on IDEAS

    as
    1. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    2. Prasad Naik & Chih‐Ling Tsai, 2000. "Partial least squares estimator for single‐index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 763-771.
    3. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    4. Heij, Christiaan & van Dijk, Dick & Groenen, Patrick J.F., 2008. "Macroeconomic forecasting with matched principal components," International Journal of Forecasting, Elsevier, vol. 24(1), pages 87-100.
    5. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    6. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    7. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
    8. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    9. Kang, In-Bong, 2003. "Multi-period forecasting using different models for different horizons: an application to U.S. economic time series data," International Journal of Forecasting, Elsevier, vol. 19(3), pages 387-400.
    10. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, 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. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.

    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. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    2. Chevillon, Guillaume, 2009. "Multi-step forecasting in emerging economies: An investigation of the South African GDP," International Journal of Forecasting, Elsevier, vol. 25(3), pages 602-628, July.
    3. Eliana González Molano & Luis Fernando Melo Velnadia & Anderson Grajales Olarte, 2007. "Pronósticos directos de la inflación colombiana," Borradores de Economia 4246, Banco de la Republica.
    4. Franses, Ph.H.B.F., 2006. "Forecasting 1 to h steps ahead using partial least squares," Econometric Institute Research Papers EI 2006-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    6. Hitesh Doshi & Kris Jacobs & Rui Liu, 2021. "Information in the Term Structure: A Forecasting Perspective," Management Science, INFORMS, vol. 67(8), pages 5255-5277, August.
    7. Chevillon, Guillaume & Hendry, David F., 2005. "Non-parametric direct multi-step estimation for forecasting economic processes," International Journal of Forecasting, Elsevier, vol. 21(2), pages 201-218.
    8. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    9. Guillaume Chevillon, 2006. "Multi-step Forecasting in Unstable Economies: Robustness Issues in the Presence of Location Shifts," Economics Series Working Papers 257, University of Oxford, Department of Economics.
    10. Proietti, Tommaso, 2011. "Direct and iterated multistep AR methods for difference stationary processes," International Journal of Forecasting, Elsevier, vol. 27(2), pages 266-280, April.
    11. 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.
    12. John Haywood & Granville Tunnicliffe Wilson, 2009. "A test for improved multi‐step forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 682-707, November.
    13. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    14. Dalibor Stevanovic & Rachidi Kotchoni & Maxime Leroux, 2017. "Forecasting economic activity in data-rich environment," CIRANO Working Papers 2017s-05, CIRANO.
    15. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    16. Hendry, David F. & Hubrich, Kirstin, 2006. "Forecasting economic aggregates by disaggregates," Working Paper Series 589, European Central Bank.
    17. Tommaso Proietti, 2016. "The Multistep Beveridge--Nelson Decomposition," Econometric Reviews, Taylor & Francis Journals, vol. 35(3), pages 373-395, March.
    18. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.
    19. Alfred A. Haug & Christie Smith, 2012. "Local Linear Impulse Responses for a Small Open Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(3), pages 470-492, June.
    20. Daoui Marouane, 2023. "Macroeconomic Forecasting using Dynamic Factor Models: The Case of Morocco," Papers 2302.14180, arXiv.org, revised May 2023.

    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:jecsur:v:24:y:2010:i:3:p:389-401. 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=0950-0804 .

    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.