Forecast-error-based estimation of forecast uncertainty when the horizon is increased

Recently, several institutions have increased their forecast horizons, and many institutions rely on their past forecast errors to estimate measures of forecast uncertainty. This work addresses the question how the latter estimation can be accomplished if there are only very few errors available for the new forecast horizons. It extends upon the results of Knüppel (2014) in order to relax the condition on the data structure required for the SUR estimator to be independent from unknown quantities. It turns out that the SUR estimator of forecast uncertainty tends to deliver large e¢ ciency gains compared to the OLS estimator (i.e. the sample mean of the squared forecast errors) in the case of increased forecast horizons. The SUR estimator is applied to the forecast errors of the Bank of England and the FOMC.