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Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility

Author

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  • Joshua C.C. Chan
  • Xuewen Yu

Abstract

We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the entire support of the joint distribution. In a Monte Carlo study we show that the new global approximation is over an order of magnitude more accurate than existing alternatives. We illustrate the proposed methodology with an application of a 96-variable VAR with stochastic volatility to measure global bank network connectedness. Our measure is able to detect the drastic increase in global bank network connectedness much earlier than rolling-window estimates from a homoscedastic VAR.

Suggested Citation

  • Joshua C.C. Chan & Xuewen Yu, 2020. "Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility," CAMA Working Papers 2020-108, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2020-108
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    File URL: https://crawford.anu.edu.au/sites/default/files/2025-05/108_2020_Chan_Yu.pdf
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    Cited by:

    1. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2023. "Forecasting using variational Bayesian inference in large vector autoregressions with hierarchical shrinkage," International Journal of Forecasting, Elsevier, vol. 39(1), pages 346-363.
    2. Chaya Weerasinghe & Ruben Loaiza-Maya & Gael M. Martin & David T. Frazier, 2023. "ABC-based Forecasting in State Space Models," Monash Econometrics and Business Statistics Working Papers 12/23, Monash University, Department of Econometrics and Business Statistics.
    3. David T. Frazier & Ruben Loaiza-Maya & Gael M. Martin, 2021. "Variational Bayes in State Space Models: Inferential and Predictive Accuracy," Papers 2106.12262, arXiv.org, revised Feb 2022.
    4. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2022. "Smoothing volatility targeting," Papers 2212.07288, arXiv.org.
    5. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    6. Flavio Pérez Rojo & Gabriel Rodríguez, 2023. "Jane Haldimand Marcet: Impact of Monetary Policy Shocks in the Peruvian Economy Over Time," Documentos de Trabajo / Working Papers 2023-523, Departamento de Economía - Pontificia Universidad Católica del Perú.
    7. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    8. Joshua C. C. Chan, 2024. "BVARs and stochastic volatility," Chapters, in: Michael P. Clements & Ana Beatriz Galvão (ed.), Handbook of Research Methods and Applications in Macroeconomic Forecasting, chapter 3, pages 43-67, Edward Elgar Publishing.
    9. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Efficient variational approximations for state space models," Papers 2210.11010, arXiv.org, revised Jun 2023.
    10. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    11. Lin Deng & Michael Stanley Smith & Worapree Maneesoonthorn, 2023. "Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns," Papers 2308.05564, arXiv.org, revised Jul 2024.
    12. Jan Prüser & Florian Huber, 2024. "Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 269-291, March.
    13. Zheng, Tingguo & Ye, Shiqi & Hong, Yongmiao, 2023. "Fast estimation of a large TVP-VAR model with score-driven volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    14. Pérez Rojo, Flavio & Rodríguez, Gabriel, 2024. "Impact of monetary policy shocks in the Peruvian economy over time," Structural Change and Economic Dynamics, Elsevier, vol. 71(C), pages 270-288.
    15. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    16. Ter Steege, Lucas, 2024. "Variational inference for Bayesian panel VAR models," Working Paper Series 2991, European Central Bank.
    17. 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.
    18. Weerasinghe, Chaya & Loaiza-Maya, Rubén & Martin, Gael M. & Frazier, David T., 2025. "ABC-based forecasting in misspecified state space models," International Journal of Forecasting, Elsevier, vol. 41(1), pages 270-289.

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    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
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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