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Variational Bayes inference in high-dimensional time-varying parameter models

Author

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  • Gary Koop

    (University of Strathclyde, UK; Rimini Centre for Economic Analysis)

  • Dimitris Korobilis

    (University of Essex, UK; Rimini Centre for Economic Analysis)

Abstract

This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.

Suggested Citation

  • Gary Koop & Dimitris Korobilis, 2018. "Variational Bayes inference in high-dimensional time-varying parameter models," Working Paper series 18-31, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:18-31
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    2. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
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    5. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen V.K. Rombouts, 2015. "The Contribution of Structural Break Models to Forecasting Macroeconomic Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 596-620, June.
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    10. Miguel A.G. Belmonte & Gary Koop & Dimitris Korobilis, 2014. "Hierarchical Shrinkage in Time‐Varying Parameter Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 80-94, January.
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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. 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.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2020. "Computationally efficient inference in large Bayesian mixed frequency VARs," Economics Letters, Elsevier, vol. 191(C).
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    6. David T. Frazier & Ruben Loaiza-Maya & Gael M. Martin & Bonsoo Koo, 2021. "Loss-Based Variational Bayes Prediction," Papers 2104.14054, arXiv.org, revised May 2022.
    7. Badi H. Baltagi & Georges Bresson & Jean-Michel Etienne, 2020. "Growth Empirics: a Bayesian Semiparametric Model With Random Coefficients for a Panel of OECD Countries," Advances in Econometrics, in: Essays in Honor of Cheng Hsiao, volume 41, pages 217-253, Emerald Group Publishing Limited.
    8. Reza Hajargasht, 2019. "Approximation Properties of Variational Bayes for Vector Autoregressions," Papers 1903.00617, arXiv.org.
    9. Korobilis, Dimitris, 2018. "Machine Learning Macroeconometrics A Primer," Essex Finance Centre Working Papers 22666, University of Essex, Essex Business School.
    10. 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.
    11. Chaya Weerasinghe & Ruben Loaiza-Maya & Gael M. Martin & David T. Frazier, 2023. "ABC-based Forecasting in State Space Models," Monash Econometrics and Business Statistics Working Papers 12/23, Monash University, Department of Econometrics and Business Statistics.
    12. Florian Huber & Gary Koop & Michael Pfarrhofer, 2020. "Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations," Papers 2002.10274, arXiv.org.
    13. 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 School of Economics.
    14. 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.
    15. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Efficient variational approximations for state space models," Papers 2210.11010, arXiv.org, revised Jun 2023.
    16. Matteo Iacopini & Luca Rossini, 2019. "Bayesian nonparametric graphical models for time-varying parameters VAR," Papers 1906.02140, arXiv.org.
    17. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    dynamic linear model; approximate posterior inference; dynamic variable selection; forecasting;
    All these keywords.

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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