Assessing Uncertainty from Point Forecasts

The paper develops a model for combining point forecasts into a predictive distribution for a variable of interest. Our approach allows for point forecasts to be correlated and admits uncertainty on the distribution parameters given the forecasts. Further, it provides an easy way to compute an augmentation factor needed to equate the dispersion of the point forecasts to that of the predictive distribution, which depends on the correlation between the point forecasts and on the number of forecasts. We show that ignoring dependence or parameter uncertainty can lead to assuming an unrealistically narrow predictive distribution. We further illustrate the implications in a newsvendor context, where our model leads to an order quantity that has higher variance but is biased in the less costly direction, and generates an increase in expected profit relative to other methods.