Approximating fixed-horizon forecasts using fixed-event forecasts

In recent years, survey-based measures of expectations and disagreement have received increasing attention in economic research. Many forecast surveys ask their participants for fixed-event forecasts. Since fixed-event forecasts have seasonal properties, researchers often use an ad-hoc approach in order to approximate fixed-horizon forecasts using fixed-event forecasts. In this work, we derive an optimal approximation by minimizing the mean-squared approximation error. Like the approximation based on the ad-hoc approach, our approximation is constructed as a weighted sum of the fixed-event forecasts, with easily computable weights. The optimal weights tend to differ substantially from those of the ad-hoc approach. In an empirical application, it turns out that the gains from using optimal instead of ad-hoc weights are very pronounced. While our work focusses on the approximation of fixedhorizon forecasts by fixed-event forecasts, the proposed approximation method is very flexible. The forecast to be approximated as well as the information employed by the approximation can be any linear function of the underlying high-frequency variable. In contrast to the ad-hoc approach, the proposed approximation method can make use of more than two such informationcontaining functions.