IDEAS home Printed from https://ideas.repec.org/a/adr/anecst/y2016i123-124p333-361.html
   My bibliography  Save this article

Sparse Graphical Vector Autoregression: A Bayesian Approach

Author

Listed:
  • Daniel Felix Ahelegbey
  • Monica Billio
  • Roberto Casarin

Abstract

This paper considers a sparsity approach for inference in large vector autoregressive (VAR) models. The approach is based on a Bayesian procedure and a graphical representation of VAR models. We discuss a Markov chain Monte Carlo algorithm for sparse graph selection, parameter estimation, and equation-specific lag selection. We show the efficiency of our algorithm on simulated data and illustrate the effectiveness of our approach in forecasting macroeconomic time series and in measuring contagion risk among financial institutions.

Suggested Citation

  • 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.
  • Handle: RePEc:adr:anecst:y:2016:i:123-124:p:333-361
    DOI: 10.15609/annaeconstat2009.123-124.0333
    as

    Download full text from publisher

    File URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.123-124.0333
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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. Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary Policy in Real Time," NBER Chapters,in: NBER Macroeconomics Annual 2004, Volume 19, pages 161-224 National Bureau of Economic Research, Inc.
    3. Gary M. Koop, 2013. "Forecasting with Medium and Large Bayesian VARS," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 177-203, March.
    4. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    5. Stock, James H. & Watson, Mark W., 2014. "Estimating turning points using large data sets," Journal of Econometrics, Elsevier, vol. 178(P2), pages 368-381.
    6. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, vol. 19(2), pages 685-738.
    7. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    8. Selva Demiralp & Kevin D. Hoover, 2003. "Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 745-767, December.
    9. Alessio Moneta, 2008. "Graphical causal models and VARs: an empirical assessment of the real business cycles hypothesis," Empirical Economics, Springer, vol. 35(2), pages 275-300, September.
    10. Diebold, Francis X. & Yılmaz, Kamil, 2014. "On the network topology of variance decompositions: Measuring the connectedness of financial firms," Journal of Econometrics, Elsevier, vol. 182(1), pages 119-134.
    11. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    12. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    13. Gefang, Deborah, 2014. "Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage," International Journal of Forecasting, Elsevier, vol. 30(1), pages 1-11.
    14. repec:sbe:breart:v:16:y:1996:i:1:a:2878 is not listed on IDEAS
    15. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    16. Wang, Hao, 2010. "Sparse seemingly unrelated regression modelling: Applications in finance and econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2866-2877, November.
    17. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    18. Alberto Roverato, 2002. "Hyper Inverse Wishart Distribution for Non-decomposable Graphs and its Application to Bayesian Inference for Gaussian Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 391-411.
    19. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306.
    20. 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.
    21. 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.
    22. Billio, Monica & Getmansky, Mila & Lo, Andrew W. & Pelizzon, Loriana, 2012. "Econometric measures of connectedness and systemic risk in the finance and insurance sectors," Journal of Financial Economics, Elsevier, vol. 104(3), pages 535-559.
    23. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    24. MArcelo C. Medeiros & Eduardo F.Mendes, 2012. "Estimating High-Dimensional Time Series Models," Textos para discussão 602, Department of Economics PUC-Rio (Brazil).
    25. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
    26. 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.
    27. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    28. Xin Huang & Hao Zhou & Haibin Zhu, 2012. "Systemic Risk Contributions," Journal of Financial Services Research, Springer;Western Finance Association, vol. 42(1), pages 55-83, October.
      • Xin Huang & Hao Zhou & Haibin Zhu, 2011. "Systemic risk contributions," BIS Papers chapters,in: Bank for International Settlements (ed.), Macroprudential regulation and policy, volume 60, pages 36-43 Bank for International Settlements.
    29. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for High-Dimensional Sparse Econometric Models," Papers 1201.0220, arXiv.org.
    30. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
    31. Bhaskar DasGupta & Lakshmi Kaligounder, 2012. "On Global Stability of Financial Networks," Papers 1208.3789, arXiv.org, revised Aug 2014.
    32. repec:hrv:faseco:33192198 is not listed on IDEAS
    33. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
    34. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," SFB 649 Discussion Papers SFB649DP2011-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    35. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," Papers 1106.3915, arXiv.org.
    36. Gary Koop & Simon Potter, 2004. "Forecasting in dynamic factor models using Bayesian model averaging," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 550-565, December.
    37. Elliott, Graham & Gargano, Antonio & Timmermann, Allan, 2013. "Complete subset regressions," Journal of Econometrics, Elsevier, vol. 177(2), pages 357-373.
    38. Guido Consonni & Luca La Rocca, 2012. "Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 743-756, December.
    39. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
    40. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
    41. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
    42. Carvalho, Carlos M. & Chang, Jeffrey & Lucas, Joseph E. & Nevins, Joseph R. & Wang, Quanli & West, Mike, 2008. "High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1438-1456.
    43. Donatello Telesca & Peter Müller & Steven M. Kornblau & Marc A. Suchard & Yuan Ji, 2012. "Modeling Protein Expression and Protein Signaling Pathways," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1372-1384, December.
    44. repec:eme:aecozz:s0731-905320140000034007 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".

    More about this item

    Keywords

    Large VAR; Model Selection; Prior Distribution; Sparse Graphical Models;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • G01 - Financial Economics - - General - - - Financial Crises
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:adr:anecst:y:2016:i:123-124:p:333-361. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Laurent Linnemer). General contact details of provider: http://edirc.repec.org/data/ensaefr.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.