Forecasting with leading indicators revisited

Transfer function or distributed lag models are commonly used in forecasting. The stability of a constant-coefficient transfer function model, however, may become an issue for many economic variables due in part to the recent advance in technology and improvement in efficiency in data collection and processing. In this paper, we propose a simple functional-coefficient transfer function model that can accommodate the changing environment. A likelihood ratio statistic is used to test the stability of a traditional transfer function model. We investigate the performance of the test statistic in the finite sample case via simulation. Using some well-known examples, we demonstrate clearly that the proposed functional-coefficient model can substantially improve the accuracy of out-of-sample forecasts. In particular, our simple modification results in a 25% reduction in the mean squared errors of out-of-sample one-step-ahead forecasts for the gas-furnace data of Box and Jenkins.