Often a forecaster has supplementary information (e.g. field reports or forecasts from another source) that cannot be included directly in a time series model. Especially interesting are cases where this information is given at time intervals that are different from those of the time series model forecasts. Previous authors have considered a numerical and a modelbased statistical method for combining extra-model information of this type with ARIMA model forecasts. This paper extends both methods to vector ARMA model forecasts and dynamic regression (transfer function) model forecasts. It is also shown that a Lagrange multiplier numerical procedure arises as a special case of the model-based procedure. An empirical example is given KEY WORDS ARIMA models Benchmarking Composite forecasts Distributed lag regression Dynamic regression Transfer function Vector ARMA Statistical time series models are widely used for forecasting. Often a forecaster has additional information that cannot be included directly in the model. Of special interest is information observed at irregular intervals (e.g. certain types of field information) or at intervals that are super-or subintervals of the time series model forecasts (e.g. annual forecasts from another source versus monthly time series model forecasts). This paper considers methods for adjusting time series model forecasts to reflect such extra-model information. The following examples illustrate potential applications:
(1) Weekly interest rate forecasts from a vector ARMA model are adjusted so that the forecasts at longer lead times are close to a quarterly 'consensus of experts' forecast.
The result takes into account the historical accuracy of the consensus forecasts.
Monthly sales forecasts from a dynamic regression are combined with an annual forecast from another source. The regression captures the month-to-month response of sales to changes in orders, but it contains little information about the annual trend. The adjusted monthly forecasts reflect the annual forecast from the second source and its error variance.