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Adaptive Hierarchical Priors for High-Dimensional Vector Autoregessions

Author

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  • Dimitris Korobilis

    () (University of Essex)

  • Davide Pettenuzzo

    () (Brandeis University)

Abstract

This paper proposes a scalable and simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal posterior distributions. We apply the algorithm to derive analytical expressions for popular Bayesian shrinkage priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The proposed algorithm is modular, parallelizable, and scales linearly with the number of predictors, allowing fast and efficient estimation of large Bayesian VARs. The benefits of our approach are explored and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. Finally, we show that our approach can be used successfully for structural analysis and can replicate important features of structural shocks predicted by economic theory.

Suggested Citation

  • Dimitris Korobilis & Davide Pettenuzzo, 2017. "Adaptive Hierarchical Priors for High-Dimensional Vector Autoregessions," Working Papers 115, Brandeis University, Department of Economics and International Businesss School.
  • Handle: RePEc:brd:wpaper:115
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    File URL: http://www.brandeis.edu/economics/RePEc/brd/doc/Brandeis_WP115.pdf
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    Cited by:

    1. Mike Tsionas & Marwan Izzeldin & Lorenzo Trapani, 2019. "Bayesian estimation of large dimensional time varying VARs using copulas," Papers 1912.12527, arXiv.org.
    2. Korobilis, Dimitris & Pettenuzzo, Davide, 2020. "Machine Learning Econometrics: Bayesian algorithms and methods," MPRA Paper 100165, University Library of Munich, Germany.
    3. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    4. Joshua C. C. Chan, 2019. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs," CAMA Working Papers 2019-61, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    5. Sebastian Ankargren & Paulina Jon'eus, 2019. "Estimating Large Mixed-Frequency Bayesian VAR Models," Papers 1912.02231, arXiv.org.
    6. Barbara Rossi, 2019. "Forecasting in the Presence of Instabilities: How Do We Know Whether Models Predict Well and How to Improve Them," Working Papers 1162, Barcelona Graduate School of Economics.
    7. Matteo Mogliani & Anna Simoni, 2019. "Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction," Papers 1903.08025, arXiv.org, revised Jun 2020.
    8. Dimitrios P. Louzis, 2019. "Steady‐state modeling and macroeconomic forecasting quality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 285-314, March.
    9. Follett, Lendie & Yu, Cindy, 2019. "Achieving parsimony in Bayesian vector autoregressions with the horseshoe prior," Econometrics and Statistics, Elsevier, vol. 11(C), pages 130-144.
    10. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano, 2019. "Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors," Journal of Econometrics, Elsevier, vol. 212(1), pages 137-154.
    11. Gupta, Rangan & Sun, Xiaojin, 2020. "Forecasting economic policy uncertainty of BRIC countries using Bayesian VARs," Economics Letters, Elsevier, vol. 186(C).
    12. Korobilis, Dimitris, 2018. "Machine Learning Macroeconometrics A Primer," Essex Finance Centre Working Papers 22666, University of Essex, Essex Business School.

    More about this item

    Keywords

    Bayesian VAR's; Mixture priors; large datasets; macroeconomic forecasting;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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