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Empirical simultaneous confidence regions for path-forecasts

Author

Listed:
  • Jordà, Òscar
  • Knüppel, Malte
  • Marcellino, Massimiliano
Abstract
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

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    10. Constantin Burgi, 2016. "What Do We Lose When We Average Expectations?," Working Papers 2016-013, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    11. 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.
    12. Filippeli, Thomai & Harrison, Richard & Theodoridis, Konstantinos, 2020. "DSGE-based priors for BVARs and quasi-Bayesian DSGE estimation," Econometrics and Statistics, Elsevier, vol. 16(C), pages 1-27.
    13. Knüppel, Malte, 2018. "Forecast-error-based estimation of forecast uncertainty when the horizon is increased," International Journal of Forecasting, Elsevier, vol. 34(1), pages 105-116.
    14. 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.
    15. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Paul Doukhan & Gabriel Lang & Anne Leucht & Michael H. Neumann, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 290-314, May.
    16. Thomai Filippeli, 2011. "Theoretical Priors for BVAR Models & Quasi-Bayesian DSGE Model Estimation," 2011 Meeting Papers 396, Society for Economic Dynamics.
    17. Diego Fresoli, 2022. "Bootstrap VAR forecasts: The effect of model uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 279-293, March.
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    19. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
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    More about this item

    Keywords

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