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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. --

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2010,06.

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Date of creation: 2010
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Handle: RePEc:zbw:bubdp1:201006

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

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  1. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, Elsevier, vol. 17(2), pages 247-267.
  2. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 15(4), pages 101-115, Fall.
  3. Massimiliano Marcellino & James Stock & Mark Watson, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," Working Papers 285, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  4. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, Elsevier, vol. 15(4), pages 393-403, October.
  5. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, Elsevier, vol. 6(2), pages 229-239, July.
  6. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 25(4), pages 449-465, 07.
  7. 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, De Gruyter, vol. 5(1), pages 1-20, August.
  8. Jushan Bai & Serena Ng, 2001. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Boston College Working Papers in Economics, Boston College Department of Economics 501, Boston College Department of Economics.
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Cited by:
  1. Tara M. Sinclair & H.O. Stekler, 2011. "Examining the Quality of Early GDP Component Estimates," Working Papers 2011-001, The George Washington University, Department of Economics, Research Program on Forecasting, revised Dec 2011.
  2. Thomai Filippeli, 2011. "Theoretical Priors for BVAR Models & Quasi-Bayesian DSGE Model Estimation," 2011 Meeting Papers, Society for Economic Dynamics 396, Society for Economic Dynamics.
  3. Tara M. Sinclair & H.O. Stekler, 2011. "Differences in Early GDP Component Estimates Between Recession and Expansion," Working Papers, The George Washington University, Institute for International Economic Policy 2011-05, The George Washington University, Institute for International Economic Policy.

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