Is there an optimal forecast combination?

We consider several geometric approaches for combining forecasts in large samples - a simple eigenvector approach, a mean corrected eigenvector and trimmed eigenvector approach. We give conditions where geometric approach yields identical result as the regression approach. We also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination. Monte Carlos are conducted to compare the finite sample performance of these and some popular forecast combination and information combination methods and to shed light on the issues of "forecast combination" vs "information combination". We also try to shed light on whether there exists an optimal forecast combination method by comparing various forecast combination methods to predict US real output growth rate and excess equity premium.