IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v59y1997i1p237-254.html
   My bibliography  Save this article

Fitting Time Series Models by Minimizing Multistep‐ahead Errors: a Frequency Domain Approach

Author

Listed:
  • J. Haywood
  • G. Tunnicliffe Wilson

Abstract

This paper brings together two topics in the estimation of time series forecasting models: the use of the multistep‐ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization. The methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients. This includes the IMA(1, 1) model for which the common exponentially weigh‐ted moving average predictor is optimal, besides more general structural models for series exhibiting trends and seasonality. The method is extended to include the Box–Jenkins `air line' model. The value of the multistep criterion is that it provides protection against using an incorrectly specified model. The value of frequency domain estimation is that the iteratively reweighted least squares scheme for fitting generalized linear models is readily extended to construct the parameter estimates and their standard errors. It also yields insight into the loss of efficiency when the model is correct and the robustness of the criterion against an incorrect model. A simple example is used to illustrate the method, and a real example demonstrates the extension to seasonal models. The discussion considers a diagnostic test statistic for indicating an incorrect model.

Suggested Citation

  • J. Haywood & G. Tunnicliffe Wilson, 1997. "Fitting Time Series Models by Minimizing Multistep‐ahead Errors: a Frequency Domain Approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 237-254.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:1:p:237-254
    DOI: 10.1111/1467-9868.00066
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00066
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00066?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Tommaso Proietti, 2016. "The Multistep Beveridge--Nelson Decomposition," Econometric Reviews, Taylor & Francis Journals, vol. 35(3), pages 373-395, March.
    3. Andrés Bujosa Brun & Marcos Bujosa Brun & Antonio García-Ferrer, 2013. "Mathematical framework for pseudo-spectra of linear stochastic difference equations," Documentos de Trabajo del ICAE 2013-13, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised May 2015.
    4. Pollock, D.S.G., 2018. "Stochastic processes of limited frequency and the effects of oversampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 18-29.
    5. Proietti, Tommaso, 2011. "Direct and iterated multistep AR methods for difference stationary processes," International Journal of Forecasting, Elsevier, vol. 27(2), pages 266-280.
    6. Tommaso Proietti, 2005. "Forecasting and signal extraction with misspecified models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 539-556.
    7. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    8. 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.
    9. 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.
    10. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    11. D.S.G. Pollock, 2017. "Stochastic processes of limited frequency and the effects of oversampling," Discussion Papers in Economics 17/03, Division of Economics, School of Business, University of Leicester.
    12. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    13. Miroslav Plasil, 2021. "Designing Macro-Financial Scenarios: The New CNB Framework and Satellite Models for Property Prices and Credit," Research and Policy Notes 2021/01, Czech National Bank.
    14. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    15. D.S.G. Pollock, 2010. "Oversampling of stochastic processes," Working Papers 44, Department of Applied Econometrics, Warsaw School of Economics.

    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:jorssb:v:59:y:1997:i:1:p:237-254. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: https://edirc.repec.org/data/rssssea.html .

    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.