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Sparse Bayesian vector autoregressions in huge dimensions

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  • Gregor Kastner
  • Florian Huber

Abstract

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities.

Suggested Citation

  • Gregor Kastner & Florian Huber, 2017. "Sparse Bayesian vector autoregressions in huge dimensions," Papers 1704.03239, arXiv.org, revised Dec 2019.
  • Handle: RePEc:arx:papers:1704.03239
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    1. 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.
    2. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
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    13. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2009. "On the evolution of the monetary policy transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 997-1017, April.
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    Cited by:

    1. Kastner, Gregor, 2019. "Sparse Bayesian time-varying covariance estimation in many dimensions," Journal of Econometrics, Elsevier, vol. 210(1), pages 98-115.
    2. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    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. 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.
    5. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2018. "Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates, 1970-2017," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-14, Economic Statistics Centre of Excellence (ESCoE).
    6. Florian Huber & Michael Pfarrhofer, 2018. "Dealing with cross-country heterogeneity in panel VARs using finite mixture models," Papers 1804.01554, arXiv.org, revised Mar 2019.

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