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Computationally Efficient Inference in Large Bayesian Mixed Frequency VARs

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  • Deborah Gefang
  • Gary Koop
  • Aubrey Poon

Abstract

Mixed frequency Vector Autoregressions (MF-VARs) can be used to provide timely and high frequency estimates or nowcasts of variables for which data is available at a low frequency. Bayesian methods are commonly used with MF-VARs to overcome overparameterization concerns. But Bayesian methods typically rely on computationally demanding Markov Chain Monte Carlo (MCMC) methods. In this paper, we develop Variational Bayes (VB) methods for use with MF-VARs using Dirichlet-Laplace global-local shrinkage priors. We show that these methods are accurate and computationally much more efficient than MCMC in two empirical applications involving large MF-VARs.

Suggested Citation

  • Deborah Gefang & Gary Koop & Aubrey Poon, 2020. "Computationally Efficient Inference in Large Bayesian Mixed Frequency VARs," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2020-07, Economic Statistics Centre of Excellence (ESCoE).
    • Handle: RePEc:nsr:escoed:escoe-dp-2020-07
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    References listed on IDEAS

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    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    3. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(4), pages 837-862, October.
    4. Frank Schorfheide & Dongho Song, 2015. "Real-Time Forecasting With a Mixed-Frequency VAR," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 366-380, July.
    5. John Cotter & Mark Hallam & Kamil Yilmaz, 2017. "Mixed-frequency macro-financial spillovers," Working Papers 201704, Geary Institute, University College Dublin.
    6. Götz, Thomas B. & Hauzenberger, Klemens, 2018. "Large mixed-frequency VARs with a parsimonious time-varying parameter structure," Discussion Papers 40/2018, Deutsche Bundesbank.
    7. Deborah Gefang & Gary Koop & Aubrey Poon, 2019. "Variational Bayesian inference in large Vector Autoregressions with hierarchical shrinkage," CAMA Working Papers 2019-08, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. Scott Brave & R. Andrew Butters & Alejandro Justiniano, 2016. "Forecasting Economic Activity with Mixed Frequency Bayesian VARs," Working Paper Series WP-2016-5, Federal Reserve Bank of Chicago.
    9. Korobilis, Dimitris & Koop, Gary, 2018. "Variational Bayes inference in high-dimensional time-varying parameter models," Essex Finance Centre Working Papers 22665, University of Essex, Essex Business School.
    10. 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).
    11. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    12. Bjørn Eraker & Ching Wai (Jeremy) Chiu & Andrew T. Foerster & Tae Bong Kim & Hernán D. Seoane, 2015. "Bayesian Mixed Frequency VARs," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 698-721.
    13. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2020. "Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 176-197, March.
    14. Ghysels, Eric, 2016. "Macroeconomics and the reality of mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 294-314.
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    Citations

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    Cited by:

    1. Andrea Carriero & Todd E. Clark & Marcellino Massimiliano, 2020. "Nowcasting Tail Risks to Economic Activity with Many Indicators," Working Papers 20-13R2, Federal Reserve Bank of Cleveland, revised 22 Sep 2020.
    2. Lehmann, Robert & Wikman, Ida, 2022. "Quarterly GDP Estimates for the German States," MPRA Paper 112642, University Library of Munich, Germany.
    3. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon & Ping Wu, 2023. "Incorporating Short Data into Large Mixed-Frequency VARs for Regional Nowcasting," Working Papers 2311, University of Strathclyde Business School, Department of Economics.
    4. Martin Feldkircher & Florian Huber & Michael Pfarrhofer, 2021. "Measuring the effectiveness of US monetary policy during the COVID‐19 recession," Scottish Journal of Political Economy, Scottish Economic Society, vol. 68(3), pages 287-297, July.
    5. Deborah Gefang & Stephen G. Hall & George S. Tavlas, 2022. "Fast Two-Stage Variational Bayesian Approach to Estimating Panel Spatial Autoregressive Models with Unrestricted Spatial Weights Matrices," Papers 2205.15420, arXiv.org, revised Aug 2023.
    6. Luca Barbaglia & Lorenzo Frattarolo & Niko Hauzenberger & Dominik Hirschbuehl & Florian Huber & Luca Onorante & Michael Pfarrhofer & Luca Tiozzo Pezzoli, 2024. "Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model," Papers 2401.10054, arXiv.org.
    7. Blagov, Boris & Müller, Henrik & Jentsch, Carsten & Schmidt, Torsten, 2021. "The investment narrative: Improving private investment forecasts with media data," Ruhr Economic Papers 921, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    8. Alain Hecq & Marie Ternes & Ines Wilms, 2021. "Hierarchical Regularizers for Mixed-Frequency Vector Autoregressions," Papers 2102.11780, arXiv.org, revised Mar 2022.
    9. Deborah Gefang & Stephen G. Hall & George S. Tavlas, 2023. "Identifying spatial interdependence in panel data with large N and small T," Papers 2309.03740, arXiv.org.
    10. Robert Lehmann, 2023. "READ-GER: Introducing German Real-Time Regional Accounts Data for Revision Analysis and Nowcasting," CESifo Working Paper Series 10315, CESifo.
    11. Blagov, Boris & Krause, Clara & Schmidt, Torsten & Exß, Franziska & Heinisch, Katja & Holtemöller, Oliver, 2024. "Frühzeitige Ermittlung stabiler Ergebnisse zum Bruttoinlandsprodukt bzw. realen Wirtschaftswachstum und der Bruttowertschöpfung auf Länderebene. Endbericht," RWI Projektberichte, RWI - Leibniz-Institut für Wirtschaftsforschung, number 296879.

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    More about this item

    Keywords

    Mixed Frequency; Variational inference; Vector Autoregression; Stochastic Volatility; Hierarchical Prior; Forecasting;
    All these keywords.

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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