The usefulness of heuristic N(E)RLS algorithms for combining forecasts

There exists theoretical and empirical evidence on the efficiency and robustness of Non-negativity Restricted Least Squares combinations of forecasts. However, the computational complexity of the method hinders its widespread use in practice. We examine various optimizing and heuristic computational algorithms for estimating NRLS combination models and provide certain CPU-time reducing implementations. We empirically compare the combination weights identified by the alternative algorithms and their computational demands based on a total of more than 66,000 models estimated to combine the forecasts of 37 firm-specific accounting earnings series. The ex ante prediction accuracies of combined forecasts from the optimizing versus heuristic algorithms are compared. The effects of fit sample size, model specification, multicollinearity, correlations of forecast errors, and series and forecast variances on the relative accuracy of the optimizing versus heuristic algorithms are analysed. The results reveal that, in general, the computationally simple heuristic algorithms perform as well as the optimizing algorithms. No generalizable conclusions could be reached, however, about which algorithm should be used based on series and forecast characteristics.