IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2011021.html
   My bibliography  Save this paper

Hierarchical shrinkage priors for dynamic regressions with many predictors

Author

Listed:
  • KOROBILIS, Dimitris

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the forecasting properties of Bayesian shrinkage in regressions with many predictors. Results show that for particular data series hierarchical shrinkage dominates factor model forecasts, and hence is a valuable addition to existing methods for handling large dimensional data.

Suggested Citation

  • KOROBILIS, Dimitris, 2011. "Hierarchical shrinkage priors for dynamic regressions with many predictors," LIDAM Discussion Papers CORE 2011021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2011021
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2011.html
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, November.
    3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    4. 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.
    5. 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.
    6. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    7. Richard F. MacLehose & David B. Dunson, 2010. "Bayesian Semiparametric Multiple Shrinkage," Biometrics, The International Biometric Society, vol. 66(2), pages 455-462, June.
    8. Pierre-Philippe Combes & Thierry Mayer & Jacques-François Thisse, 2008. "Economic Geography: The Integration of Regions and Nations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00311000, HAL.
    9. Inoue, Atsushi & Kilian, Lutz, 2008. "How Useful Is Bagging in Forecasting Economic Time Series? A Case Study of U.S. Consumer Price Inflation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 511-522, June.
    10. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203, Decembrie.
    11. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    12. 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.
    13. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    14. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, November.
    15. Robert B. Litterman, 1979. "Techniques of forecasting using vector autoregressions," Working Papers 115, Federal Reserve Bank of Minneapolis.
    16. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    17. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    18. 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.
    19. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    20. Artin Armagan & Russell Zaretzki, 2010. "Model selection via adaptive shrinkage with t priors," Computational Statistics, Springer, vol. 25(3), pages 441-461, September.
    21. 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, November.
    22. Hobert, James P. & Geyer, Charles J., 1998. "Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 414-430, November.
    23. 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.
    24. 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, April.
    25. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    Full references (including those not matched with items on IDEAS)

    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. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    2. Dimitris Korobilis, 2018. "Machine Learning Macroeconometrics: A Primer," Working Paper series 18-30, Rimini Centre for Economic Analysis.
    3. Sandra Stankiewicz, 2015. "Forecasting Euro Area Macroeconomic Variables with Bayesian Adaptive Elastic Net," Working Paper Series of the Department of Economics, University of Konstanz 2015-12, Department of Economics, University of Konstanz.
    4. Gilles Celeux & Mohammed El Anbari & Jean-Michel Marin & Christian P. Robert, 2010. "Regularization in Regression : Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation," Working Papers 2010-43, Center for Research in Economics and Statistics.
    5. Barbara Rossi, 2019. "Forecasting in the presence of instabilities: How do we know whether models predict well and how to improve them," Economics Working Papers 1711, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2021.
    6. Kim, Hyun Hak & Swanson, Norman R., 2014. "Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence," Journal of Econometrics, Elsevier, vol. 178(P2), pages 352-367.
    7. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    8. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    9. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Elliott, Graham & Gargano, Antonio & Timmermann, Allan, 2013. "Complete subset regressions," Journal of Econometrics, Elsevier, vol. 177(2), pages 357-373.
    11. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    12. Aijun Yang & Ju Xiang & Lianjie Shu & Hongqiang Yang, 2018. "Sparse Bayesian Variable Selection with Correlation Prior for Forecasting Macroeconomic Variable using Highly Correlated Predictors," Computational Economics, Springer;Society for Computational Economics, vol. 51(2), pages 323-338, February.
    13. Baragatti, M. & Pommeret, D., 2012. "A study of variable selection using g-prior distribution with ridge parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1920-1934.
    14. Yen-Shiu Chin & Ting-Li Chen, 2016. "Minimizing variable selection criteria by Markov chain Monte Carlo," Computational Statistics, Springer, vol. 31(4), pages 1263-1286, December.
    15. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
    16. Zhang, Yaojie & Ma, Feng & Wang, Yudong, 2019. "Forecasting crude oil prices with a large set of predictors: Can LASSO select powerful predictors?," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 97-117.
    17. Hyun Hak Kim & Norman Swanson, 2013. "Mining Big Data Using Parsimonious Factor and Shrinkage Methods," Departmental Working Papers 201316, Rutgers University, Department of Economics.
    18. Chakraborty, Sounak & Lozano, Aurelie C., 2019. "A graph Laplacian prior for Bayesian variable selection and grouping," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 72-91.
    19. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    20. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.

    More about this item

    Keywords

    forecasting; shrinkage; factor model; variable selection; Bayesian LASSO;
    All these keywords.

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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:cor:louvco:2011021. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.