Robust Optimization of Forecast Combinations

A methodology is developed for constructing robust forecast combinations which improve upon a given benchmark specification for all symmetric and convex loss functions. The optimal forecast combination asymptotically almost surely dominates the benchmark and, in addition, minimizes the expected loss function, under standard regularity conditions. The optimum in a given sample can be found by solving a large Convex Optimization problem. An application to forecasting of changes of the S&P 500 Volatility Index shows that robust optimized combinations improve significantly upon the out-of-sample forecasting accuracy of simple averaging and unrestricted optimization.