Split-then-Combine simplex combination and selection of forecasters

TL;DR

This paper introduces a novel forecast combination method within the simplex space, enhancing forecast accuracy especially when sample sizes are small, by comparing it with traditional methods and proposing a selection approach.

Contribution

It develops the Split-Then-Combine approach in the simplex space and introduces a Combine-After-Selection method for efficient forecast combination and selection.

Findings

Simplicial center outperforms fixed-weight averages

CAS method effectively reduces redundant forecasters

Method is useful with small sample sizes

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.