The problem of finding appropriate weights to combine several density forecasts
is an important issue currently debated in the forecast combination literature.
Recently, a paper by Hall and Mitchell (IJF, 2007) proposes to combine density
forecasts with optimal weights obtained from solving an optimization problem.
This paper studies the properties of this optimization problem when the number
of forecasting periods is relatively small and finds that it often produces corner
solutions by allocating all the weight to one density forecast only. This paper’s
practical recommendation is to have an additional training sample period for the
optimal weights. While reserving a portion of the data for parameter estimation
and making pseudo-out-of-sample forecasts are common practices in the empirical
literature, employing a separate training sample for the optimal weights is novel,
and it is suggested because it decreases the chances of corner solutions. Alternative
log-score or quadratic-score weighting schemes do not have this training sample