Optimal Updating of Forecasts for the Timing of Future Events

A major problem in forecasting is estimating the time of some future event. Traditionally, forecasts are designed to minimize an error cost function that is evaluated once, possibly when the event occurs and forecast accuracy can be determined. However, in many applications forecast error costs accumulate over time, and the forecasts themselves may be updated with information that is collected as the expected time of the event approaches. This paper examines one such application, in which flow control managers in the U.S. air traffic system depend on forecasts of aircraft departure times to predict and alleviate potential congestion. These forecasts are periodically updated until take-off occurs, although the number of updates may be limited by the cost of collecting, processing, and distributing information. The procedures developed in this paper balance the costs of accumulated forecast errors and the costs of forecast updates. The procedures are applied to the aircraft departure forecasting problem and are compared with methods currently used by the air traffic management system. Numerical examples demonstrate that the procedures increase forecast accuracy while reducing the costs associated with frequent forecast updates.