From Reactive to Proactive Volatility Modeling With Hemisphere Neural Networks
提出一种半球神经网络架构，通过共享核心、波动强调约束和阻塞式现实检验，实现宏观经济密度预测的最大似然估计，在点预测和密度预测上优于经典和现代机器学习模型。
ABSTRACT We revisit maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE work in this context. First, the hemispheres share a common core at the entrance of the network, which accommodates various forms of time variation in the error variance. Second, we introduce a volatility emphasis constraint that breaks mean/variance indeterminacy in this class of overparametrized nonlinear models. Third, we conduct a blocked out‐of‐bag reality check to curb overfitting in both conditional moments. Fourth, the algorithm utilizes standard deep learning software and thus handles large data sets‐both computationally and statistically. Ergo, our hemisphere neural network (HNN) provides proactive volatility forecasts based on leading indicators when it can, and reactive volatility based on the magnitude of previous prediction errors when it must. We evaluate point and density forecasts with an extensive out‐of‐sample experiment and benchmark against a suite of models ranging from classics to more modern machine learning‐based offerings. In all cases, HNN fares well by consistently providing accurate mean/variance forecasts for all targets and horizons. Studying the resulting volatility paths reveals its versatility, while probabilistic forecasting evaluation metrics showcase its enviable reliability. Finally, we also demonstrate how this machinery can be merged with other structured deep learning models by revisiting Goulet Coulombe (2025)'s neural Phillips curve.