Split-then-Combine simplex combination and selection of forecasters

Abstract

This paper considers the Split-Then-Combine (STC) approach (Arroyo and de Juan, 2014) to combine forecasts inside the simplex space, the sample space of positive weights adding up to one. As it turns out, the simplicial statistic given by the center of the simplex compares favorably against the fixed-weight, average forecast. Besides, we also develop a Combine-After-Selection (CAS) method to get rid of redundant forecasters. We apply these two approaches to make out-of-sample one-step ahead combinations and subcombinations of forecasts for several economic variables. This methodology is particularly useful when the sample size is smaller than the number of forecasts, a case where other methods (e.g., Least Squares (LS) or Principal Component Analysis (PCA)) are not applicable.