From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks

57 Pages Posted: 29 Nov 2023 Last revised: 23 Apr 2024

See all articles by Philippe Goulet Coulombe

Philippe Goulet Coulombe

Université du Québec à Montréal - Département des Sciences Économiques

Mikael Frenette

University of Quebec at Montreal (UQAM) - Department of Economics

Karin Klieber

Oesterreichische Nationalbank (OeNB)

Date Written: November 9, 2023

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.

Keywords: neural networks, uncertainty, density forecasting, macroeconomics, maximum likelihood

JEL Classification: C14, C22, C45, C55, E37

Suggested Citation

Goulet Coulombe, Philippe and Frenette, Mikael and Klieber, Karin, From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks (November 9, 2023). Available at SSRN: https://ssrn.com/abstract=4627773 or http://dx.doi.org/10.2139/ssrn.4627773

Philippe Goulet Coulombe (Contact Author)

Université du Québec à Montréal - Département des Sciences Économiques ( email )

PB 8888 Station DownTown
Succursale Centre Ville
Montreal, Quebec H3C3P8
Canada

Mikael Frenette

University of Quebec at Montreal (UQAM) - Department of Economics ( email )

3150, rue Jean-Brillant
Montreal, Quebec H3T 1N8
Canada

Karin Klieber

Oesterreichische Nationalbank (OeNB) ( email )

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