Beating the Simple Average: Egalitarian LASSO for Combining Economic Forecasts

Despite the clear success of forecast combination in many economic environments,
several important issues remain incompletely resolved. The issues relate to selection of
the set of forecasts to combine, and whether some form of additional regularization (e.g.,
shrinkage) is desirable. Against this background, and also considering the frequently-found
superiority of simple-average combinations, we propose LASSO-based procedures that select
and shrink toward equal combining weights. We then provide an empirical assessment of
the performance of our "egalitarian LASSO" procedures. The results indicate that simple
averages are highly competitive, and that although out-of-sample RMSE improvements on
simple averages are possible in principle using our methods, they are hard to achieve in real
time, due to the intrinsic difficulty of small-sample real-time cross validation of the LASSO
tuning parameter. We therefore propose alternative direct combination procedures, most
notably \best average" combination, motivated by the structure of egalitarian LASSO and
the lessons learned, which do not require choice of a tuning parameter yet outperform simple

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