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Large Order-Invariant Bayesian VARs with Stochastic Volatility

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  • Joshua C. C. Chan
  • Gary Koop
  • Xuewen Yu

Abstract

Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way the variables are ordered due to the use of a lower triangular parameterization of the error covariance matrix. We show that the order invariance problem in existing approaches is likely to become more serious in large VARs. We propose the use of a specification which avoids the use of this lower triangular parameterization. We show that the presence of multivariate stochastic volatility allows for identification of the proposed model and prove that it is invariant to ordering. We develop a Markov chain Monte Carlo algorithm which allows for Bayesian estimation and prediction. In exercises involving artificial and real macroeconomic data, we demonstrate that the choice of variable ordering can have non-negligible effects on empirical results when using the nonorder invariant approach. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our order-invariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, non-order invariant, approach.

Suggested Citation

  • Joshua C. C. Chan & Gary Koop & Xuewen Yu, 2024. "Large Order-Invariant Bayesian VARs with Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 825-837, April.
  • Handle: RePEc:taf:jnlbes:v:42:y:2024:i:2:p:825-837
    DOI: 10.1080/07350015.2023.2252039
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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. Joshua Chan & Eric Eisenstat & Xuewen Yu, 2022. "Large Bayesian VARs with Factor Stochastic Volatility: Identification, Order Invariance and Structural Analysis," Papers 2207.03988, arXiv.org.
    3. 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.
    4. 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.
    5. Florian Huber & Gary Koop & Massimiliano Marcellino & Tobias Scheckel, 2024. "Bayesian modelling of VAR precision matrices using stochastic block networks," Papers 2407.16349, arXiv.org.
    6. Chenghan Hou & Bao Nguyen & Bo Zhang, 2023. "Real‐time forecasting of the Australian macroeconomy using flexible Bayesian VARs," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 418-451, March.
    7. Florian Huber & Gary Koop, 2023. "Fast and Order-invariant Inference in Bayesian VARs with Non-Parametric Shocks," Working Papers 2309, University of Strathclyde Business School, Department of Economics.
    8. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Shin, Minchul, 2023. "Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1054-1086.
    9. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    10. Ping Wu & Gary Koop, 2022. "Fast, Order-Invariant Bayesian Inference in VARs using the Eigendecomposition of the Error Covariance Matrix," Working Papers 2310, University of Strathclyde Business School, Department of Economics.
    11. Helmut Lutkepohl & Fei Shang & Luis Uzeda & Tomasz Wo'zniak, 2024. "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference," Papers 2404.11057, arXiv.org.
    12. Luis Gruber & Gregor Kastner, 2022. "Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!," Papers 2206.04902, arXiv.org, revised Jul 2023.
    13. Prüser, Jan & Blagov, Boris, 2022. "Improving inference and forecasting in VAR models using cross-sectional information," Ruhr Economic Papers 960, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    14. Wu, Ping & Koop, Gary, 2023. "Estimating the ordering of variables in a VAR using a Plackett–Luce prior," Economics Letters, Elsevier, vol. 230(C).
    15. Braun, Robin, 2021. "The importance of supply and demand for oil prices: evidence from non-Gaussianity," Bank of England working papers 957, Bank of England.
    16. Uddin, Mohammad Jalal, 2023. "Investigating the impulse responses of renewable energy in the context of China: A Bayesian VAR Approach," Renewable Energy, Elsevier, vol. 219(P2).

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