Optimal and robust combination of forecasts via constrained optimization and shrinkage

We introduce various methods that combine forecasts using constrained optimization with penalty. A non-negativity constraint is imposed on the weights, and several penalties are considered, taking form of a divergence from reference combination scheme. In contrast most existing approaches, our framework performs forecast selection in one step, allowing for potentially sparse combining schemes. Moreover, by exploiting analogy between portfolio optimization, we provide analytical expression optimal penalty strength when penalizing L2-divergence equally-weighted An extensive simulation study two empirical applications allow us to investigate impact function, scheme, predictive performance. Our results suggest proposed models outperform those considered previous studies.