Resumen de Compositional combination and selection of forecasters
Antonio S. Martín Arroyo, Aranzazu de Juan Fernández
The Split-Then-Combine approach has previously been used to generate the weights of forecasts in a combination in the Euclidean space. This paper extends this approach 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 sample centre compares favourably against the fixed-weight, average forecast. Besides, we also develop a Combination-After-Selection method to get rid of redundant forecasters. We apply these 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., ordinary least squares or principal component analysis) are not applicable.
