Linear Hybrid Shrinkage of Weights for Forecast Selection and Combination

Abstract

Forecast combination is an established methodology to improve forecast accuracy. The primary questions in the current literature are how many and which forecasts to include (selection) and how to weight the selected forecasts (weighting). Although integrating both tasks seems appealing, we are only aware of a few data analytical models that integrate both tasks. We introduce Linear Hybrid Shrinkage (LHS), a novel method that uses information criteria from statistical learning theory to select forecasters and then shrinks the selection from their in-sample optimal weights linearly towards equality, while shrinking the non-selected forecasts towards zero. Simulation results show conditions (scenarios) where LHS leads to higher accuracy than LASSO-based Shrinkage, Linear Shrinkage of in-sample optimal weights, and a simple averaging of forecasts.