Shaping forecast models for arbitrary choice of bandwidth

原文摘要

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 have been widely 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, which usually depends only on the bandwidth, and the finite sample bias-variance trade-off, which depends jointly on the kernel shape as well as the bandwidth. When 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. To this end we establish that a class of affine kernel shapes indexed by a single parameter, s, is optimal under squared forecast error loss. We 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 in practice. 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.

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