Using density forecasts to improve mean forecasts

We propose a method to improve a given conditional mean forecast with a given density forecast by estimating functional regressions. Our method offers a feasible and rigorous way of aligning conditional mean forecasts with the underlying distributional risks or uncertainties. It relies on functional principal components (FPCs) as an effective way to summarize and exploit the predictive content of density forecasts. We perform an application to forecasting the United States quarterly GDP growth rate. We consider the Survey of Professional Forecasters (SPF)’ consensus (average) forecast as a point forecast. Our results show more than 30% improvement in the out-of-sample (OOS) root mean square (forecasting) error for one-year-ahead GDP growth rate by using our functional regression forecasts relative to the SPF’s average. The main reason is the predictive content associated with recession and expansion periods which helps decreasing the OOS bias. Our findings suggest that the SPF’s consensus (average) forecast tends to be conservative.