Empirical Simultaneous Confidence Regions for Path-Forecasts
AbstractMeasuring 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 con.dence bands around the Fed and Bank of England real-time path-forecasts of growth and inflation.
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Bibliographic InfoPaper provided by European University Institute in its series Economics Working Papers with number ECO2010/18.
Date of creation: 2010
Date of revision:
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path forecast; forecast uncertainty; simultaneous confidence region; Scheffé’s S-method; Mahalanobis distance; false discovery rate.;
Other versions of this item:
- Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2010. "Empirical Simultaneous Confidence Regions for Path-Forecasts," CEPR Discussion Papers 7797, C.E.P.R. Discussion Papers.
- Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2010. "Empirical simultaneous confidence regions for path-forecasts," Discussion Paper Series 1: Economic Studies 2010,06, Deutsche Bundesbank, Research Centre.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-11 (All new papers)
- NEP-CBA-2010-06-11 (Central Banking)
- NEP-ECM-2010-06-11 (Econometrics)
- NEP-ETS-2010-06-11 (Econometric Time Series)
- NEP-FOR-2010-06-11 (Forecasting)
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