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VAR Forecasting Using Bayesian Variable Selection

  • Dimitris Korobilis

    (Université Catholique de Louvain; The Rimini Centre for Economic Analysis (RCEA))

This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data-based restrictions of VAR coefficients can help improve upon their unrestricted counterparts in forecasting, and in many cases they compare favorably to shrinkage estimators.

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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 51_10.

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Date of creation: Jan 2010
Date of revision: Apr 2011
Handle: RePEc:rim:rimwps:51_10
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  1. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
  2. Anthony Garratt & Gary Koop & Emi Mise & Shaun Vahey, 2008. "Real-time Prediction with UK Monetary Aggregates in the Presence of Model Uncertainty," Reserve Bank of New Zealand Discussion Paper Series DP2008/13, Reserve Bank of New Zealand.
  3. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
  4. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen Rombouts, 2011. "A comparison of Forecasting Procedures for Macroeconomic Series: The Contribution of Structural Break Models," Working Papers 1113, University of Strathclyde Business School, Department of Economics.
  5. Gary Koop & Dimitris Korobilis, 2009. "Forecasting Inflation Using Dynamic Model Averaging," Working Paper Series 34_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  6. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
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  9. Jan J. J. Groen & Richard Paap & Francesco Ravazzolo, 2009. "Real-time inflation forecasting in a changing world," Staff Reports 388, Federal Reserve Bank of New York.
  10. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
  11. Gary Koop & Dimitris Korobilis, 2009. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Working Paper Series 47_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  12. Canova, Fabio & Ciccarelli, Matteo, 2004. "Forecasting and turning point predictions in a Bayesian panel VAR model," Journal of Econometrics, Elsevier, vol. 120(2), pages 327-359, June.
  13. Joshua C.C. Chan & Garry Koop & Roberto Leon Gonzales & Rodney W. Strachan, 2010. "Time Varying Dimension Models," ANU Working Papers in Economics and Econometrics 2010-523, Australian National University, College of Business and Economics, School of Economics.
  14. Todd E. Clark & Michael W. McCracken, 2006. "Averaging forecasts from VARs with uncertain instabilities," Research Working Paper RWP 06-12, Federal Reserve Bank of Kansas City.
  15. Gary Koop & Simon M. Potter, 2007. "Estimation and Forecasting in Models with Multiple Breaks," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 763-789.
  16. Gambetti, Luca & D’Agostino, Antonello & Giannone, Domenico, 2010. "Macroeconomic forecasting and structural change," Working Paper Series 1167, European Central Bank.
  17. Jochmann, Markus & Koop, Gary & Strachan, Rodney W., 2010. "Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks," International Journal of Forecasting, Elsevier, vol. 26(2), pages 326-347, April.
  18. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  19. Martha Banbura & Domenico Giannone & Lucrezia Reichlin, 2008. "Large Bayesian VARs," Working Papers ECARES 2008_033, ULB -- Universite Libre de Bruxelles.
  20. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
  21. Cogley, Timothy & Morozov, Sergei & Sargent, Thomas J., 2005. "Bayesian fan charts for U.K. inflation: Forecasting and sources of uncertainty in an evolving monetary system," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1893-1925, November.
  22. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  23. K. J. Martijn Cremers, 2002. "Stock Return Predictability: A Bayesian Model Selection Perspective," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1223-1249.
  24. Canova, Fabio & Gambetti, Luca, 2009. "Structural changes in the US economy: Is there a role for monetary policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 477-490, February.
  25. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
  26. 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.
  27. Korobilis, Dimitris, 2008. "Forecasting in vector autoregressions with many predictors," MPRA Paper 21122, University Library of Munich, Germany.
  28. Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.
  29. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  30. 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.
  31. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
  32. 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.
  33. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2009. "On the evolution of the monetary policy transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 997-1017, April.
  34. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
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