Choosing a Coverage Probability for Prediction Intervals

Coverage probabilities for prediction intervals are germane to filtering, forecasting, previsions, regression, and time series analysis. It is a common practice to choose the coverage probabilities for such intervals by convention or by astute judgment. We argue here that coverage probabilities can be chosen by decision theoretic considerations. But to do so, we need to specify meaningful utility functions. Some stylized choices of such functions are given, and a prototype approach is presented.