Philippe Goulet Coulombe, Mikael Frenette, Karin Klieber
arXiv 27 Nov 2023 · Econometrics · 3 citations (OpenAlex)
arXiv:2311.16333 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Goulet Coulombe, P (2022) A neural phillips curve and a deep output gap | 0.984 | 21 | 7 | 95% |
| 2 | Belkin, M., Hsu, D., Ma, S., and Mandal, S (2019) Reconciling modern machine-learning practice and the classical bias–variance trade-off | 0.928 | 4 | 3 | 100% |
| 3 | Adrian, T., Boyarchenko, N., and Giannone, D (2019) Vulnerable growth | 0.874 | 5 | 2 | 100% |
| 4 | Knüppel, M., Krüger, F., and Pohle, M.-O (2022) Score-based calibration testing for multivariate forecast distributions | 0.737 | 4 | 2 | 75% |
| 5 | Goulet Coulombe, P (2020) The macroeconomy as a random forest | 0.737 | 3 | 3 | 67% |
| 6 | Salinas, D., Flunkert, V., Gasthaus, J., and Januschowski, T (2020) Deepar: Probabilistic forecasting with autoregressive recurrent networks | 0.737 | 3 | 3 | 67% |
| 7 | Chan, J. C., Koop, G., and Potter, S. M (2016) A bounded model of time variation in trend inflation, nairu and the phillips curve | 0.737 | 3 | 2 | 100% |
| 8 | Guidolin, M., La Cara, D., and Marcellino, M. G (2021) Boosting the forecasting power of conditional heteroskedasticity models to account for covid-19 outbreaks | 0.737 | 3 | 2 | 100% |
| 9 | Chipman, H. A., George, E. I., and McCulloch, R. E (2010) Bart: Bayesian additive regression trees | 0.644 | 4 | 2 | 50% |
| 10 | Goulet Coulombe, P (2020) Time-varying parameters as ridge regressions | 0.644 | 2 | 2 | 100% |
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