Composite Forecasting: An Integrated Approach and Optimality Reconsidered

This article shows when the theoretical Lagrange multiplier solution for combining forecasts has a regression representation. This solution is not optimal in general because it imposes a restriction on an otherwise more general linear form. The optimal linear predictor based on N forecasts is presented. This predictor is or is not a regression function depending on whether the latter function is linear. I also show that the Lagrange multiplier solution may often be nearly optimal. Hence, when estimating a composite forecast, the restriction imposed by this solution may prove useful. This observation is supported in an empirical example.