Path Forecast Evaluation
نویسندگان
چکیده
A forecast path refers to the vector of forecasts over the next 1 to h periods into the future. These forecasts are correlated across horizons so that to properly understand the uncertainty associated with the forecast path, one requires the joint predictive density of the path rather than the collection of marginal predictive densities for each horizon. This paper derives the joint predictive density for forecasts generated with VARs or with direct forecast methods from possibly infinite order data generating processes. Given this density, we use Scheffé’s S-method to construct simultaneous confidence regions for the forecast path and show how to construct path forecasts conditional on assumed paths for a subset of the system’s variables, along with their conditional predictive density and a test on the assumed path’s likelihood. We then introduce the mean square forecast path metric to compare the predictive ability between competing models, and appropriately modify Diebold-Mariano-West and Giacomini-White predictive ability tests. Finally, as empirical illustrations of the theoretical concepts, we evaluate path forecasts from a system of U.S. macroeconomic variables, and examine the role of monetary aggregates in forecasting inflation. JEL Classification Codes: C32, C52, C53
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