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Empirical simultaneous confidence regions for path-forecasts

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  • 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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    Cited by:

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    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. Svetlana Makarova, 2014. "Risk and Uncertainty: Macroeconomic Perspective," UCL SSEES Economics and Business working paper series 129, UCL School of Slavonic and East European Studies (SSEES).
    5. Lee, Seohyun, 2017. "Three essays on uncertainty: real and financial effects of uncertainty shocks," MPRA Paper 83617, University Library of Munich, Germany.
    6. Thomai Filippeli, 2011. "Theoretical Priors for BVAR Models & Quasi-Bayesian DSGE Model Estimation," 2011 Meeting Papers 396, Society for Economic Dynamics.
    7. Filippeli, Thomai & Harrison, Richard & Theodoridis, Konstantinos, 2018. "DSGE-based Priors for BVARs & Quasi-Bayesian DSGE Estimation," Cardiff Economics Working Papers E2018/5, Cardiff University, Cardiff Business School, Economics Section.
    8. 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.
    9. 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.
    10. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    11. 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.
    12. Veiga, Helena & Ruiz, Esther & Gonçalves Mazzeu, Joao Henrique, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. 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.

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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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