Working Paper: CEPR ID: DP7797
Authors: Scar Jord; Malte Knüppel; Massimiliano Marcellino
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: forecast uncertainty; path forecast; Scheffé's method; simultaneous confidence region
JEL Codes: C32; C52; C53
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| sample size (C83) | accuracy of confidence regions (C13) |
| traditional confidence bands (C46) | coverage rates (G22) |
| empirical Scheffé bands (C46) | performance in controlling FDR (H12) |
| Bonferroni bounds (C46) | performance for FWE control (C69) |
| Bonferroni bounds (C46) | performance for FDR control (C22) |