Probability Forecasts Made at Multiple Lead Times

Many probability forecasts are revised as new information becomes available, generating a time series of forecasts for a single event. Although methods for evaluating probability forecasts have been extensively studied, they apply to a single forecast per event. This paper is the first to evaluate probability forecasts that are made—and therefore revised—at many lead times for a single event. I postulate a norm for multi-period probability-forecasting systems and derive properties that should hold regardless of the forecasting process. I use these properties to develop methods for evaluating a forecasting system based on a sample. I apply these methods to the National Hurricane Center’s wind-speed probability forecasts and to statistical election forecasts, finding evidence that both can be improved using the current set of predictors.