Combining distributions of real-time forecasts: An application to U.S. growth

We extend the repeated observations forecasting (ROF) analysis of Croushore and Stark (2002) to allow for regressors of possibly higher sampling frequencies than the regressand. For the U.S. GNP quarterly growth rate, we compare the forecasting performances of an AR model with several mixed-frequency models among which is the MIDAS approach. Using the additional dimension provided by different vintages we compute several forecasts for a given calendar date and subsequently approximate the corresponding distribution of forecasts by a continuous density. Scoring rules are then employed to construct combinations of them and analyze the composition and evolvement of the implied weights over time. Using this approach, we not only investigate the sensitivity of model selection to the choice of which data release to consider, but also illustrate how to incorporate revision process information into real-time studies. As a consequence of these analyses, we
introduce a new weighting scheme that summarizes information contained in the revision process of the variables under consideration.