An empirical analysis of the accuracy of SA, OLS, ERLS and NRLS combination forecasts

Theoretically, the efficiency of OLS combination forecasts can be improved by imposing linear equality or nonnegativity restrictions on the combination weights. In Equality Restricted Least Squares (ERLS) combinations, the weights are restricted to sum to unity, whereas in Nonnegativity Restricted Least Squares (NRLS) combinations, the weights are constrained to be nonnegative. There is little empirical evidence on the relative performance of OLS, ERLS and NRLS combination forecasts. In this study, the authors provide empirical results on the relative accuracy of OLS, ERLS, NRLS and Simple Average (SA) ex ante combined forecasts using three macroeconomic and thirty-seven firm specific series. The empirical results reveal that combined forecasts are not always more accurate. NRLS and SA combinations almost always outperform OLS and ERLS combinations, while NRLS combinations are at least as robust and accurate as SA combinations. On average, ERLS combination models without a constant term produce more accurate forecasts than OLS combination models.