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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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7797.

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Date of creation: Apr 2010
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Handle: RePEc:cpr:ceprdp:7797
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  1. Marcellino, Massimiliano & Stock, James H & Watson, Mark W, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," CEPR Discussion Papers 4976, C.E.P.R. Discussion Papers.
  2. 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, 07.
  3. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
  4. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
  5. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
  6. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  7. 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.
  8. 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.
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