A note on the estimation of optimal weights for density forecast combinations

The problem of finding appropriate weights for combining several density forecasts is an important issue that is currently being debated in the forecast combination literature. A recent paper by Hall and Mitchell (2007) proposes that density forecasts be combined using the weights obtained from solving an optimization problem. This paper documents the properties of this optimization problem through a series of simulation experiments. When the number of forecasting periods is relatively small, the optimization problem often produces solutions that are dominated by a number of simple alternatives.