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Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage

Author

Listed:
  • Deborah Gefang

  • Gary Koop

  • Aubrey Poon

Abstract

Many recent papers in macroeconomics have used large Vector Autoregressions (VARs) involving a hundred or more dependent variables. With so many parameters to estimate, Bayesian prior shrinkage is vital in achieving reasonable results. Computational concerns currently limit the range of priors used and render difficult the addition of empirically important features such as stochastic volatility to the large VAR. In this paper, we develop variational Bayes methods for large VARs which overcome the computational hurdle and allow for Bayesian inference in large VARs with a range of hierarchical shrinkage priors and with time-varying volatilities. We demonstrate the computational feasibility and good forecast performance of our methods in an empirical application involving a large quarterly US macroeconomic data set.

Suggested Citation

  • Deborah Gefang & Gary Koop & Aubrey Poon, 2019. "Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage," Discussion Papers in Economics 19/05, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:19/05
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp19-05.pdf
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    Cited by:

    1. Chan, Joshua C.C. & Yu, Xuewen, 2022. "Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    2. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2022. "Smoothing volatility targeting," Papers 2212.07288, arXiv.org.
    3. Deborah Gefang & Stephen G Hall & George S. Tavlas, 2025. "Estimating unrestricted spatial interdependence in panel spatial autoregressive models with latent common factors," Papers 2510.22399, arXiv.org.
    4. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2020. "Computationally efficient inference in large Bayesian mixed frequency VARs," Economics Letters, Elsevier, vol. 191(C).
    5. Matteo Iacopini & Luca Rossini, 2019. "Bayesian nonparametric graphical models for time-varying parameters VAR," Papers 1906.02140, arXiv.org.
    6. Joshua C. C. Chan, 2019. "Large Bayesian Vector Autoregressions," CAMA Working Papers 2019-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. 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.
    8. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    9. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2024. "Variational Inference for Large Bayesian Vector Autoregressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1066-1082, July.

    More about this item

    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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