Too similar to combine? On negative weights in forecast combination

Abstract

This paper provides the first thorough investigation of the negative weights that can emerge when combining forecasts. The usual practice in the literature is to consider only convex combinations and ignore or trim negative weights, i.e., set them to zero. This default strategy has its merits, but it is not optimal. We study the problem from various angles, and the main conclusion is that negative weights emerge when highly correlated forecasts with similar variances are combined. In this situation, the estimated weights have large variances, and trimming reduces the variance of the weights and improves the combined forecast. The threshold of zero is arbitrary and can be improved. We propose an optimal trimming threshold, i.e., an additional tuning parameter to improve forecasting performance. The effects of optimal trimming are demonstrated in simulations. In the empirical example using the European Central Bank Survey of Professional Forecasters, we find that the new strategy performs exceptionally well and can deliver improvements of more than 10% for inflation, up to 20% for GDP growth, and more than 20% for unemployment forecasts relative to the equal-weight benchmark.