Optimal Forecast Combinations Under General Loss Functions and Forecast Error Distributions
U of California, Econ, Discussion Paper No. 2002-08
56 Pages Posted: 30 Jul 2002
Date Written: April 29, 2002
Existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss. Under this loss function empirical studies have generally found that estimates of optimal forecast combination weights lead to higher losses than equally-weighted combined forecasts which in turn outperform the best individual predictions. We show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed. We characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights. We also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise.
Keywords: Forecast Combination, Asymmetric Loss, Inflation Forecasting
JEL Classification: C13, C93
Suggested Citation: Suggested Citation