| Abstract: |
We reinvigorate 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 for 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 (2022)'s Neural Phillips Curve. |