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Empirical simultaneous confidence regions for path-forecasts


  • Jordà, Òscar
  • Knüppel, Malte
  • Marcellino, Massimiliano


Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that the variable may follow over time is summarized by the simultaneous confidence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one cannot derive analytic expressions for this confidence region, and its non-parametric estimation is impractical given commonly available predictive sample sizes. Instead, this paper derives the approximate rectangular confidence regions that control false discovery rate error, which are a function of the predictive sample covariance matrix and the empirical distribution of the Mahalanobis distance of the path-forecast errors. These rectangular regions are simple to construct and appear to work well in a variety of cases explored empirically and by simulation. The proposed techniques are applied to provide confidence bands around the Fed and Bank of England real-time path-forecasts of growth and inflation.

Suggested Citation

  • Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2010. "Empirical simultaneous confidence regions for path-forecasts," Discussion Paper Series 1: Economic Studies 2010,06, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdp1:201006

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    References listed on IDEAS

    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. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    3. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    4. Rubin Daniel & Dudoit Sandrine & van der Laan Mark, 2006. "A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-20, August.
    5. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
    6. 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.
    7. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
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    Cited by:

    1. 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.
    2. Sinclair, Tara M. & Stekler, H.O. & Carnow, Warren, 2015. "Evaluating a vector of the Fed’s forecasts," International Journal of Forecasting, Elsevier, vol. 31(1), pages 157-164.
    3. Sinclair, Tara M. & Stekler, H.O., 2013. "Examining the quality of early GDP component estimates," International Journal of Forecasting, Elsevier, vol. 29(4), pages 736-750.
    4. Thomai Filippeli, 2011. "Theoretical Priors for BVAR Models & Quasi-Bayesian DSGE Model Estimation," 2011 Meeting Papers 396, Society for Economic Dynamics.
    5. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    6. Tara M. Sinclair & H.O. Stekler, 2011. "Differences in Early GDP Component Estimates Between Recession and Expansion," Working Papers 2011-05, The George Washington University, Institute for International Economic Policy.

    More about this item


    Path forecast; forecast uncertainty; simultaneous confidence region; Scheffé's S-method; Mahalanobis distance; false discovery rate;

    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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