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Adaptive Hierarchical Priors for High-Dimensional Vector Autoregessions


  • Dimitris Korobilis

    () (University of Essex)

  • Davide Pettenuzzo

    () (Brandeis University)


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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    References listed on IDEAS

    1. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?," CEPR Discussion Papers 5829, C.E.P.R. Discussion Papers.
    2. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    3. repec:wly:japmet:v:25:y:2010:i:1:p:71-92 is not listed on IDEAS
    4. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
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    Cited by:

    1. Matteo Mogliani, 2019. "Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction," Papers 1903.08025,
    2. repec:eee:ecosta:v:11:y:2019:i:c:p:130-144 is not listed on IDEAS
    3. 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.
    4. repec:wly:japmet:v:34:y:2019:i:2:p:285-314 is not listed on IDEAS
    5. Korobilis, Dimitris, 2018. "Machine Learning Macroeconometrics A Primer," Essex Finance Centre Working Papers 22666, University of Essex, Essex Business School.

    More about this item


    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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