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Empirical simultaneous confidence regions for path-forecasts

Oscar Jorda (), Malte Knüppel and Massimiliano Marcellino

No 2010,06, Discussion Paper Series 1: Economic Studies from Deutsche Bundesbank

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.

Keywords: Path forecast; forecast uncertainty; simultaneous confidence region; Scheffé's S-method; Mahalanobis distance; false discovery rate (search for similar items in EconPapers)
JEL-codes: C32 C52 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cba, nep-ecm and nep-for
Date: 2010
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Related works:
Journal Article: Empirical simultaneous prediction regions for path-forecasts (2013) Downloads
Working Paper: Empirical simultaneous prediction regions for path-forecasts (2012) Downloads
Working Paper: Empirical Simultaneous Confidence Regions for Path-Forecasts (2010) Downloads
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