IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v192y2016i2p374-390.html
   My bibliography  Save this article

Large Bayesian VARMAs

Author

Listed:
  • Chan, Joshua C.C.
  • Eisenstat, Eric
  • Koop, Gary

Abstract

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this field. In this paper, we develop a Bayesian approach for inference in VARMAs which surmounts these problems. It jointly ensures identification and parsimony in the context of an efficient Markov chain Monte Carlo (MCMC) algorithm. We use this approach in a macroeconomic application involving up to twelve dependent variables. We find our algorithm to work successfully and provide insights beyond those provided by VARs.

Suggested Citation

  • Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2016. "Large Bayesian VARMAs," Journal of Econometrics, Elsevier, vol. 192(2), pages 374-390.
    • Handle: RePEc:eee:econom:v:192:y:2016:i:2:p:374-390
    DOI: 10.1016/j.jeconom.2016.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407616300082
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2016.02.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Marta Bańbura, 2008. "Large Bayesian VARs," 2008 Meeting Papers 334, Society for Economic Dynamics.
    3. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, November.
    4. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    5. D.S. Poskitt & Wenying Yao, 2012. "VAR Modeling and Business Cycle Analysis: A Taxonomy of Errors," Monash Econometrics and Business Statistics Working Papers 11/12, Monash University, Department of Econometrics and Business Statistics.
    6. 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.
    7. Bai, Jushan & Wang, Peng, 2012. "Identification and estimation of dynamic factor models," MPRA Paper 38434, University Library of Munich, Germany.
    8. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    9. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Bayesian VARs: Specification Choices and Forecast Accuracy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 46-73, January.
    10. Giannone, Domenico & Lenza, Michele & Momferatou, Daphne & Onorante, Luca, 2014. "Short-term inflation projections: A Bayesian vector autoregressive approach," International Journal of Forecasting, Elsevier, vol. 30(3), pages 635-644.
    11. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    13. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    14. Carriero, A. & Kapetanios, G. & Marcellino, M., 2009. "Forecasting exchange rates with a large Bayesian VAR," International Journal of Forecasting, Elsevier, vol. 25(2), pages 400-417.
    15. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    16. Peiris, M. Shelton, 1988. "On the study of some functions of multivariate ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 146-151, April.
    17. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    18. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    19. 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, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    20. Koop, Gary, 2014. "Forecasting with dimension switching VARs," International Journal of Forecasting, Elsevier, vol. 30(2), pages 280-290.
    21. van Dyk, David A. & Park, Taeyoung, 2008. "Partially Collapsed Gibbs Samplers: Theory and Methods," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 790-796, June.
    22. 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.
    23. Cooley, Thomas F. & Dwyer, Mark, 1998. "Business cycle analysis without much theory A look at structural VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 57-88.
    24. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    25. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    26. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-723, July.
    27. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    28. Gefang, Deborah, 2014. "Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage," International Journal of Forecasting, Elsevier, vol. 30(1), pages 1-11.
    29. Athanasopoulos, George & Vahid, Farshid, 2008. "VARMA versus VAR for Macroeconomic Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 237-252, April.
    30. George, Edward I. & Sun, Dongchu & Ni, Shawn, 2008. "Bayesian stochastic search for VAR model restrictions," Journal of Econometrics, Elsevier, vol. 142(1), pages 553-580, January.
    31. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    32. Konstantinos Metaxoglou & Aaron Smith, 2007. "Maximum Likelihood Estimation of VARMA Models Using a State‐Space EM Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 666-685, September.
    33. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    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. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2021. "Bayesian Local Projections," The Warwick Economics Research Paper Series (TWERPS) 1348, University of Warwick, Department of Economics.
    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. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    4. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "The Transmission of Monetary Policy Shocks," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 74-107, July.
    5. Joshua C. C. Chan, 2020. "Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 68-79, January.
    6. Dufays, Arnaud & Rombouts, Jeroen V.K., 2020. "Relevant parameter changes in structural break models," Journal of Econometrics, Elsevier, vol. 217(1), pages 46-78.
    7. Benati, Luca & Chan, Joshua & Eisenstat, Eric & Koop, Gary, 2020. "Identifying noise shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    8. Joshua C. C. Chan, 2019. "Large Bayesian vector autoregressions," CAMA Working Papers 2019-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    10. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    11. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    12. Mike Tsionas & Marwan Izzeldin & Lorenzo Trapani, 2019. "Bayesian estimation of large dimensional time varying VARs using copulas," Papers 1912.12527, arXiv.org.
    13. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    14. Chan, Joshua C.C. & Poon, Aubrey & Zhu, Dan, 2023. "High-dimensional conditionally Gaussian state space models with missing data," Journal of Econometrics, Elsevier, vol. 236(1).
    15. Matteo Iacopini & Luca Rossini, 2019. "Bayesian nonparametric graphical models for time-varying parameters VAR," Papers 1906.02140, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2014. "Large Bayesian VARMAs," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-06, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    3. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    4. Koop, Gary & Korobilis, Dimitris, 2016. "Model uncertainty in Panel Vector Autoregressive models," European Economic Review, Elsevier, vol. 81(C), pages 115-131.
    5. Gary Koop, 2012. "Using VARs and TVP-VARs with Many Macroeconomic Variables," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(3), pages 143-167, September.
    6. Joshua C.C. Chan & Eric Eisenstat, 2013. "Gibbs Samplers for VARMA and Its Extensions," ANU Working Papers in Economics and Econometrics 2013-604, Australian National University, College of Business and Economics, School of Economics.
    7. Koop, Gary & Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Bayesian compressed vector autoregressions," Journal of Econometrics, Elsevier, vol. 210(1), pages 135-154.
    8. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    10. Berg, Tim O. & Henzel, Steffen R., 2015. "Point and density forecasts for the euro area using Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1067-1095.
    11. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    12. Korobilis, Dimitris, 2016. "Prior selection for panel vector autoregressions," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 110-120.
    13. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    14. Joshua C. C. Chan, 2019. "Large Bayesian vector autoregressions," CAMA Working Papers 2019-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    15. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    16. Nima Nonejad, 2021. "An Overview Of Dynamic Model Averaging Techniques In Time‐Series Econometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 566-614, April.
    17. Koop, Gary, 2014. "Forecasting with dimension switching VARs," International Journal of Forecasting, Elsevier, vol. 30(2), pages 280-290.
    18. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    19. Joshua C. C. Chan & Eric Eisenstat & Chenghan Hou & Gary Koop, 2020. "Composite likelihood methods for large Bayesian VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 692-711, September.
    20. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    21. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.

    More about this item

    Keywords

    VARMA identification; Markov chain Monte Carlo; Bayesian; Stochastic search variable selection;
    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
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    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:eee:econom:v:192:y:2016:i:2:p:374-390. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.