IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2016-6.html
   My bibliography  Save this paper

Bayesian Rank Selection in Multivariate Regression

Author

Listed:
  • Bin Jiang

    ()

  • Anastasios Panagiotelis

    ()

  • George Athanasopoulos

    ()

  • Rob Hyndman

    ()

  • Farshid Vahid

    ()

Abstract

Estimating the rank of the coefficient matrix is a major challenge in multivariate regression, including vector autoregression (VAR). In this paper, we develop a novel fully Bayesian approach that allows for rank estimation. The key to our approach is reparameterizing the coefficient matrix using its singular value decomposition and conducting Bayesian inference on the decomposed parameters. By implementing a stochastic search variable selection on the singular values of the coefficient matrix, the ultimate selected rank can be identified as the number of nonzero singular values. Our approach is appropriate for small multivariate regressions as well as for higher dimensional models with up to about 40 predictors. In macroeconomic forecasting using VARs, the advantages of shrinkage through proper Bayesian priors are well documented. Consequently, the shrinkage approach proposed here that selects or averages over low rank coefficient matrices is evaluated in a forecasting environment. We show in both simulations and empirical studies that our Bayesian approach provides forecasts that are better than those of the most promising benchmark methods, dynamic factor models and factor augmented VARs.

Suggested Citation

  • Bin Jiang & Anastasios Panagiotelis & George Athanasopoulos & Rob Hyndman & Farshid Vahid, 2016. "Bayesian Rank Selection in Multivariate Regression," Monash Econometrics and Business Statistics Working Papers 6/16, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2016-6
    as

    Download full text from publisher

    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp06-16.pdf
    Download Restriction: no

    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. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    3. Strachan, Rodney W, 2003. "Valid Bayesian Estimation of the Cointegrating Error Correction Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 185-195, January.
    4. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier.
    5. Bernanke, Ben S & Blinder, Alan S, 1992. "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review, American Economic Association, vol. 82(4), pages 901-921, September.
    6. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    7. Robinson, P. M., 1973. "Generalized canonical analysis for time series," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 141-160, June.
    8. Sims, Christopher A., 1992. "Interpreting the macroeconomic time series facts : The effects of monetary policy," European Economic Review, Elsevier, vol. 36(5), pages 975-1000, June.
    9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    10. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    11. Andrea Carriero & George Kapetanios & Massimiliano Marcellino, 2011. "Forecasting large datasets with Bayesian reduced rank multivariate models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 735-761, August.
    12. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    13. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    14. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    15. Eric M. Leeper & Christopher A. Sims & Tao Zha, 1996. "What Does Monetary Policy Do?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 27(2), pages 1-78.
    16. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    17. 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.
    18. Patrick J. Wolfe & Simon J. Godsill & Wee-Jing Ng, 2004. "Bayesian variable selection and regularization for time-frequency surface estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 575-589.
    19. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    20. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    21. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, May.
    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. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
    24. 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.
    25. John C. Robertson & Ellis W. Tallman, 1999. "Vector autoregressions: forecasting and reality," Economic Review, Federal Reserve Bank of Atlanta, issue Q1, pages 4-18.
    26. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
    27. Robinson, P M, 1974. "Identification, Estimation and Large-Sample Theory for Regressions Containing Unobservable Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 680-692, October.
    28. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    singular value decomposition; model selection; vector autoregression; macroeconomic forecasting; dynamic factor models;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:msh:ebswps:2016-6. 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: (Dr Xibin Zhang) or (Joanne Lustig). General contact details of provider: http://edirc.repec.org/data/dxmonau.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.