Before revision:  Theoretical properties are examined and we show that non-linear synthesis improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions that are met in most real applications.
After revision:  Theoretical properties are examined and we show that non-linear synthesis improves the expected squared forecast error , we identify the conditions and mechanism for which non-linear synthesis improves over linear combinations; conditions that are met in most real applications.