Bregman model averaging for forecast combination

We propose a unified model averaging (MA) approach for a broad class of forecasting targets. This approach is established by minimizing an asymptotic risk based on the expected Bregman divergence of a combined forecast, relative to the optimal forecast of the forecasting target, under local(-to-zero) asymptotics. It can be flexibly applied to develop effective MA methods across various forecasting contexts, including but not limited to univariate and multivariate mean forecasting, volatility forecasting, probabilistic forecasting, and density forecasting. As illustrative examples, we present a series of simulation experiments and empirical cases that demonstrate strong numerical performance of our approach in forecasting.