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Path Forecast Evaluation


  • Òscar Jordà
  • Massimiliano Marcellino


A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffé’s (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.

Suggested Citation

  • Òscar Jordà & Massimiliano Marcellino, 2008. "Path Forecast Evaluation," Economics Working Papers ECO2008/34, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2008/34

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    References listed on IDEAS

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    Cited by:

    1. McCracken, Michael W. & McGillicuddy, Joseph, 2017. "An Empirical Investigation of Direct and Iterated Multistep Conditional Forecasts," Working Papers 2017-40, Federal Reserve Bank of St. Louis.
    2. Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2013. "Empirical simultaneous prediction regions for path-forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 456-468.
    3. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    4. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    5. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Michael Wolf & Dan Wunderli, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 352-376, May.
    6. Carson, Richard T. & Cenesizoglu, Tolga & Parker, Roger, 2011. "Forecasting (aggregate) demand for US commercial air travel," International Journal of Forecasting, Elsevier, vol. 27(3), pages 923-941, July.
    7. repec:eee:energy:v:141:y:2017:i:c:p:2251-2263 is not listed on IDEAS
    8. Farooq Akram & Andrew Binning & Junior Maih, 2016. "Joint Prediction Bands for Macroeconomic Risk Management," Working Papers No 5/2016, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    9. Pinson, P. & Girard, R., 2012. "Evaluating the quality of scenarios of short-term wind power generation," Applied Energy, Elsevier, vol. 96(C), pages 12-20.
    10. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2018. "Skewness-Adjusted Bootstrap Confidence Intervals and Confidence Bands for Impulse Response Functions," MAGKS Papers on Economics 201810, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    11. Schüssler, Rainer & Trede, Mark, 2016. "Constructing minimum-width confidence bands," Economics Letters, Elsevier, vol. 145(C), pages 182-185.
    12. Stefan Bruder, 2014. "Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions," ECON - Working Papers 181, Department of Economics - University of Zurich, revised Dec 2015.
    13. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
    14. repec:gam:jeners:v:10:y:2017:i:9:p:1402-:d:111989 is not listed on IDEAS
    15. Staszewska-Bystrova Anna, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 680-690, October.
    16. Matei Demetrescu & Mu-Chun Wang, 2014. "Incorporating Asymmetric Preferences into Fan Charts and Path Forecasts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(2), pages 287-297, April.
    17. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2018. "Skewness-Adjusted Bootstrap Confidence Intervals and Confidence Bands for Impulse Response Functions," Lodz Economics Working Papers 1/2018, University of Lodz, Faculty of Economics and Sociology.
    18. 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.
    19. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.
    20. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2092-1 is not listed on IDEAS
    21. Antoniadis, Anestis & Brossat, Xavier & Cugliari, Jairo & Poggi, Jean-Michel, 2016. "A prediction interval for a function-valued forecast model: Application to load forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 939-947.
    22. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.
    23. Paolo Vidoni, 2017. "Improved multivariate prediction regions for Markov process models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 1-18, March.

    More about this item


    path forecast; simultaneous confidence region; error bands;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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