Efficiency of the independence assumption in the combination of forecasts

In seeking to minimise the composite forecast error variance of a linear combination of forecasts, contradictory suggestions have been reported concerning the practice of making the assumption of independence between forecast errors. This assumption can introduce robustness though its avoidance of sampling errors in the estimation of correlation coefficient(s), although it does render the composite forecast theoretically suboptimal. By means of theory and experimental simulation, this paper examines the circumstances whereby the independence assumption may produce more efficient composite forecasts. Its applicability is shown to depend both upon the underlying correlation structure and relative size of forecast errors as well as the observation base available for estimation.