First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the Gaussian assumption. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.
Probability Forecast Combination via Entropy Regularized Wasserstein Distance
WP20-31R - We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance.