IDEAS home Printed from https://ideas.repec.org/p/ssb/dispap/871.html
   My bibliography  Save this paper

Encompassing tests for evaluating multi-step system forecasts invariant to linear transformations

Author

Listed:

Abstract

The paper suggests two encompassing tests for evaluating multi-step system forecasts invariant to linear transformations. An invariant measure for forecast accuracy is necessary as the conclusions otherwise can depend on how the forecasts are reported (e.g., as in level or growth rates). Therefore, a measure based on the prediction likelihood of the forecast for all variables at all horizons is used. Both tests are based on a generalization of the encompassing test for univariate forecasts where potential heteroscedasticity and autocorrelation in the forecasts are considered. The tests are used in evaluating quarterly multi-step system forecasts made by Statistics Norway.

Suggested Citation

  • Håvard Hungnes, 2018. "Encompassing tests for evaluating multi-step system forecasts invariant to linear transformations," Discussion Papers 871, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:871
    as

    Download full text from publisher

    File URL: https://www.ssb.no/en/forskning/discussion-papers/_attachment/340009?_ts=1617a4be268
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hendry, David F. & Martinez, Andrew B., 2017. "Evaluating multi-step system forecasts with relatively few forecast-error observations," International Journal of Forecasting, Elsevier, vol. 33(2), pages 359-372.
    2. El-Shagi, Makram & Giesen, Sebastian & Jung, Alexander, 2016. "Revisiting the relative forecast performances of Fed staff and private forecasters: A dynamic approach," International Journal of Forecasting, Elsevier, vol. 32(2), pages 313-323.
    3. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    4. Bjørnland, Hilde C. & Ravazzolo, Francesco & Thorsrud, Leif Anders, 2017. "Forecasting GDP with global components: This time is different," International Journal of Forecasting, Elsevier, vol. 33(1), pages 153-173.
    5. Christoffersen, Peter F & Diebold, Francis X, 1998. "Cointegration and Long-Horizon Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 450-458, October.
    6. Andre Jungmittag, 2016. "Combination of Forecasts across Estimation Windows: An Application to Air Travel Demand," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(4), pages 373-380, July.
    7. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 1998. "Tests for Forecast Encompassing," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 254-259, April.
    8. Henningsen, Arne & Hamann, Jeff D., 2007. "systemfit: A Package for Estimating Systems of Simultaneous Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i04).
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    10. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, January.
    11. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    12. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
    13. Anders Bredahl Kock & Timo Teräsvirta, 2016. "Forecasting Macroeconomic Variables Using Neural Network Models and Three Automated Model Selection Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1753-1779, December.
    14. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    15. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    16. David Harvey & Paul Newbold, 2000. "Tests for multiple forecast encompassing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 471-482.
    17. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    18. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    19. Ericsson Neil R., 2008. "Comment on "Economic Forecasting in a Changing World" (by Michael Clements and David Hendry)," Capitalism and Society, De Gruyter, vol. 3(2), pages 1-18, October.
    20. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    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. Magnus Kvåle Helliesen & Håvard Hungnes & Terje Skjerpen, 2022. "Revisions in the Norwegian National Accounts: accuracy, unbiasedness and efficiency in preliminary figures," Empirical Economics, Springer, vol. 62(3), pages 1079-1121, March.
    2. Håvard Hungnes, 2020. "Equal predictability test for multi-step-ahead system forecasts invariant to linear transformations," Discussion Papers 931, Statistics Norway, Research Department.
    3. Andrew B. Martinez, 2020. "Extracting Information from Different Expectations," Working Papers 2020-008, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    4. Håvard Hungnes, 2020. "Predicting the exchange rate path. The importance of using up-to-date observations in the forecasts," Discussion Papers 934, Statistics Norway, Research Department.

    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. Håvard Hungnes, 2020. "Equal predictability test for multi-step-ahead system forecasts invariant to linear transformations," Discussion Papers 931, Statistics Norway, Research Department.
    2. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    3. Busetti, Fabio & Marcucci, Juri, 2013. "Comparing forecast accuracy: A Monte Carlo investigation," International Journal of Forecasting, Elsevier, vol. 29(1), pages 13-27.
    4. Håvard Hungnes, 2020. "Predicting the exchange rate path. The importance of using up-to-date observations in the forecasts," Discussion Papers 934, Statistics Norway, Research Department.
    5. Harvey, David I. & Leybourne, Stephen J. & Whitehouse, Emily J., 2017. "Forecast evaluation tests and negative long-run variance estimates in small samples," International Journal of Forecasting, Elsevier, vol. 33(4), pages 833-847.
    6. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
    7. Jörg Breitung & Malte Knüppel, 2021. "How far can we forecast? Statistical tests of the predictive content," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(4), pages 369-392, June.
    8. Kontogeorgos, Georgios & Lambrias, Kyriacos, 2019. "An analysis of the Eurosystem/ECB projections," Working Paper Series 2291, European Central Bank.
    9. Mark E. Wohar & David E. Rapach, 2007. "Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models This is a significantly revised version of our previous paper, 'Forecasting US Business Fixed ," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(1), pages 33-51.
    10. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    11. Wang, Zijun & Bessler, David A., 2004. "Forecasting performance of multivariate time series models with full and reduced rank: an empirical examination," International Journal of Forecasting, Elsevier, vol. 20(4), pages 683-695.
    12. Rapach, David E. & Strauss, Jack K., 2012. "Forecasting US state-level employment growth: An amalgamation approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 315-327.
    13. Ali Dib & Mohamed Gammoudi & Kevin Moran, 2008. "Forecasting Canadian time series with the New Keynesian model," Canadian Journal of Economics, Canadian Economics Association, vol. 41(1), pages 138-165, February.
    14. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    15. Clements, Michael P. & Harvey, David I., 2011. "Combining probability forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 208-223.
    16. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    17. Thomas A. Knetsch, 2005. "Evaluating the German Inventory Cycle Using Data from the Ifo Business Survey," Contributions to Economics, in: Jan-Egbert Sturm & Timo Wollmershäuser (ed.), Ifo Survey Data in Business Cycle and Monetary Policy Analysis, pages 61-92, Springer.
    18. Claus Brand & Hans-Eggert Reimers & Franz Seitz, 2003. "Narrow Money and the Business Cycle: Theoretical aspects and euro area evdence," Macroeconomics 0303012, University Library of Munich, Germany.
    19. Dick van Dijk & Philip Hans Franses & Michael P. Clements & Jeremy Smith, 2003. "On SETAR non-linearity and forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(5), pages 359-375.
    20. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408, Edward Elgar Publishing.

    More about this item

    Keywords

    Macroeconomic forecasts; Econometric models; Forecast performance; Forecast evaluation; Forecast comparison;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    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:ssb:dispap:871. 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: L Maasø (email available below). General contact details of provider: https://edirc.repec.org/data/ssbgvno.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.