Abstract
Parameter instability has been widely documented to lead to poor predictive accuracy for economic forecasting models. Adaptive schemes for data weighting such as rolling-window estimation only involve a single tuning parameter (akin to a bandwidth) and are often used to address this issue. The importance of the shape of the weighting scheme (kernel) has received far less attention in the forecasting literature. In this paper we show that in practice there can be a large discrepancy between the theoretically optimal bias-variance tradeoff, based on the optimal bandwidth, and the actual bias-variance trade-off in practice, which depends jointly on the kernel shape as well as the (typically non-optimal) bandwidth. Simplifying this joint optimization problem by focusing only on one dimension, we show that optimizing over the kernel shape rather than the bandwidth often constitutes a better performing and more practical choice. We establish that a class of affine kernel shapes indexed by a single parameter, s, is optimal under squared forecast error loss, show that the shape parameter can be restricted to the interval [0, 2], where s=0 corresponds to a uniform kernel (rolling-window) and s=2 corresponds to a triangular kernel, and develop a robust three-point grid search method for choosing this shape parameter. An empirical analysis of U.S. inflation forecasting demonstrates the advantage of optimizing for the kernel shape parameter, particularly in unstable environments characterized by a time-varying bias-variance trade-off.