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Efficient selection of hyperparameters in large Bayesian VARs using automatic differentiation

Author

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  • Joshua C. C. Chan
  • Liana Jacobi
  • Dan Zhu

Abstract

Large Bayesian VARs with the natural conjugate prior are now routinely used for forecasting and structural analysis. It has been shown that selecting the prior hyperparameters in a data-driven manner can often substantially improve forecast performance. We propose a computationally efficient method to obtain the optimal hyperparameters based on Automatic Differentiation, which is an efficient way to compute derivatives. Using a large US dataset, we show that using the optimal hyperparameter values leads to substantially better forecast performance. Moreover, the proposed method is much faster than the conventional grid-search approach, and is applicable in high-dimensional optimization problems. The new method thus provides a practical and systematic way to develop better shrinkage priors for forecasting in a data-rich environment.

Suggested Citation

  • Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2019. "Efficient selection of hyperparameters in large Bayesian VARs using automatic differentiation," CAMA Working Papers 2019-46, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2019-46
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    References listed on IDEAS

    as
    1. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2022. "An automated prior robustness analysis in Bayesian model comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 583-602, April.
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    15. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2019. "How Sensitive Are VAR Forecasts to Prior Hyperparameters? An Automated Sensitivity Analysis," Advances in Econometrics, in: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A, volume 40, pages 229-248, Emerald Group Publishing Limited.
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    Cited by:

    1. Joshua C. C. Chan, 2022. "Asymmetric conjugate priors for large Bayesian VARs," Quantitative Economics, Econometric Society, vol. 13(3), pages 1145-1169, July.
    2. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    3. Chan, Joshua C.C., 2021. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1212-1226.
    4. Nadiia Shapovalenko, 2021. "A BVAR Model for Forecasting Ukrainian Inflation and GDP," Visnyk of the National Bank of Ukraine, National Bank of Ukraine, issue 251, pages 14-36.
    5. Jamie L. Cross & Chenghan Hou & Gary Koop, 2021. "Macroeconomic Forecasting with Large Stochastic Volatility in Mean VARs," Working Papers No 04/2021, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    6. Consolo, Agostino & Foroni, Claudia & Martínez Hernández, Catalina, 2021. "A mixed frequency BVAR for the euro area labour market," Working Paper Series 2601, European Central Bank.

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    More about this item

    Keywords

    automatic differentiation; vector autoregression; optimal hyperparameters; forecasts; marginal likelihood;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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