The Why and the How of Combining VAR and Survey Density Forecasts

Abstract

This paper investigates how real-time forecasts from a wide range of Bayesian vector autoregression (BVAR) specifications and survey (judgemental) forecasts can be combined by making optimal use of their properties. To this end, we compare the forecasting performance of optimal pooling and tilting techniques that incorporate survey information in various forms. We focus on the forecasting of euro area inflation and GDP growth at medium-term forecast horizons, using information from the ECB's Survey of Professional Forecasters (SPF). The results show that the SPF has a good point-prediction performance but performs poorly in terms of densities for all variables and horizons. Accordingly, when individual models are tilted to the first moments of the SPF (ex-ante) and then optimally combined, point accuracy and calibration improve, but this is not always the case when the second moments of the SPF are included in the tilting. Therefore, the judgement embedded in survey forecasts can considerably improve model prediction accuracy, but the way and extent to which it is incorporated matters and depends on the signal provided by the survey.

Keywords: Entropic tilting, Judgement, Optimal Pooling, Real Time, Survey of Professional Forecasters