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Bayesian Nonlinear Regression using Sums of Simple Functions

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  • Florian Huber

Abstract

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR.

Suggested Citation

  • Florian Huber, 2023. "Bayesian Nonlinear Regression using Sums of Simple Functions," Papers 2312.01881, arXiv.org.
  • Handle: RePEc:arx:papers:2312.01881
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    File URL: http://arxiv.org/pdf/2312.01881
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    References listed on IDEAS

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    1. Regis Barnichon & Christian Matthes & Alexander Ziegenbein, 2022. "Are the Effects of Financial Market Disruptions Big or Small?," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 557-570, May.
    2. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2024. "Addressing COVID-19 Outliers in BVARs with Stochastic Volatility," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1403-1417, September.
    3. Hamilton, James D, 2001. "A Parametric Approach to Flexible Nonlinear Inference," Econometrica, Econometric Society, vol. 69(3), pages 537-573, May.
    4. Hamilton, James D., 2003. "What is an oil shock?," Journal of Econometrics, Elsevier, vol. 113(2), pages 363-398, April.
    5. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
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    Cited by:

    1. Florian Huber & Karin Klieber & Massimiliano Marcellino & Luca Onorante & Michael Pfarrhofer, 2024. "Asymmetries in Financial Spillovers," Papers 2410.16214, arXiv.org.

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