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A Bayesian Approach to Modelling Graphical Vector Autoregressions

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  • Jukka Corander
  • Mattias Villani

Abstract

. We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation‐based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an approximate joint posterior distribution of the number of lags in the autoregression and the causality structure represented by graphs using a fractional Bayes approach. Some properties of the approximation are derived and our approach is illustrated on a four‐dimensional macroeconomic system and five‐dimensional air pollution data.

Suggested Citation

  • Jukka Corander & Mattias Villani, 2006. "A Bayesian Approach to Modelling Graphical Vector Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 141-156, January.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:141-156
    DOI: 10.1111/j.1467-9892.2005.00460.x
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    References listed on IDEAS

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    1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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    Cited by:

    1. P. Giudici & A. Spelta, 2016. "Graphical Network Models for International Financial Flows," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 128-138, January.
    2. Yin, Libo & Ma, Xiyuan, 2018. "Causality between oil shocks and exchange rate: A Bayesian, graph-based VAR approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 434-453.
    3. Tomasz Wozniak, 2016. "Rare Events and Risk Perception: Evidence from Fukushima Accident," Department of Economics - Working Papers Series 2021, The University of Melbourne.
    4. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2020. "Modeling Turning Points In Global Equity Market," DEM Working Papers Series 195, University of Pavia, Department of Economics and Management.
    5. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2012. "Bayesian Graphical Models for Structural Vector Autoregressive Processes," Working Papers 2012:36, Department of Economics, University of Venice "Ca' Foscari".
    6. Daniel Felix Ahelegbey & Paolo Giudici, 2020. "Market Risk, Connectedness and Turbulence: A Comparison of 21st Century Financial Crises," DEM Working Papers Series 188, University of Pavia, Department of Economics and Management.
    7. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Bayesian Graphical Models for STructural Vector Autoregressive Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 357-386, March.
    8. Ahelegbey, Daniel Felix, 2015. "The Econometrics of Bayesian Graphical Models: A Review With Financial Application," MPRA Paper 92634, University Library of Munich, Germany, revised 25 Apr 2016.
    9. Daniela Scidá, 2023. "Structural VAR and financial networks: A minimum distance approach to spatial modeling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(1), pages 49-68, January.
    10. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".
    11. Tomasz Woźniak, 2016. "Bayesian Vector Autoregressions," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 49(3), pages 365-380, September.
    12. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    13. Paci, Lucia & Consonni, Guido, 2020. "Structural learning of contemporaneous dependencies in graphical VAR models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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