Adaptively combined forecasting for discrete response time series

Adaptive combining is generally a desirable approach for forecasting, which, however, has rarely been explored for discrete response time series. In this paper, we propose an adaptively combined forecasting method for such discrete response data. We demonstrate in theory that the proposed forecast is of the desired adaptation with respect to the widely used squared risk and other significant risk functions under mild conditions. Furthermore, we study the issue of adaptation for the proposed forecasting method in the presence of model screening that is often useful in applications. Our simulation study and two real-world data examples show promise for the proposed approach.