Working Paper: CEPR ID: DP7009
Authors: Scar Jord; Massimiliano Marcellino
Abstract: A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffé's (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.
Keywords: Error bands; Path forecast; 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 |
|---|---|
| traditional marginal error bands (C51) | misleading representations of uncertainty (D80) |
| individual forecast errors (C53) | misleading representations of uncertainty (D80) |
| joint predictive density (C46) | better coverage of uncertainty (D80) |
| Scheffé bands (C29) | superior performance compared to traditional methods (C52) |
| accuracy of uncertainty representation (D80) | enhanced communication of forecast uncertainty (C53) |