Cumings-Menon Ryan, Shin Minchul
The US Census Bureau, 4600 Silver Hill Rd, Suitland-Silver Hill, MD 20746, USA.
Federal Reserve Bank of Philadelphia, Ten Independence Mall, Philadelphia, PA 19106, USA.
Entropy (Basel). 2020 Aug 25;22(9):929. doi: 10.3390/e22090929.
We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the assumption. More specifically, we show that the regularized Wasserstein barycenter between multivariate Gaussian input densities is multivariate Gaussian, and provide a simple way to compute mean and its variance-covariance matrix. 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.
我们提出了使用熵正则化瓦瑟斯坦距离定义的概率和密度预测组合方法。首先，在该假设下，我们基于正则化瓦瑟斯坦距离对组合密度预测进行了理论刻画。更具体地说，我们表明多元高斯输入密度之间的正则化瓦瑟斯坦重心是多元高斯的，并提供了一种计算均值及其方差协方差矩阵的简单方法。其次，我们展示了这种正则化类型如何提高所得组合密度的预测能力。第三，我们提供了一种选择控制正则化强度的调整参数的方法。最后，我们将我们提出的方法应用于美国通货膨胀率密度预测，并说明相对于未正则化的对应方法，熵正则化如何提高预测密度的质量。
