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Forecasting using a large number of predictors: is Bayesian regression a valid alternative to principal components?

  • De Mol, Christine
  • Giannone, Domenico
  • Reichlin, Lucrezia

This paper considers Bayesian regression with normal and doubleexponential priors as forecasting methods based on large panels of time series. We show that, empirically, these forecasts are highly correlated with principal component forecasts and that they perform equally well for a wide range of prior choices. Moreover, we study the asymptotic properties of the Bayesian regression under Gaussian prior under the assumption that data are quasi collinear to establish a criterion for setting parameters in a large cross-section.

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2006,32.

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Date of creation: 2006
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Handle: RePEc:zbw:bubdp1:5040
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  1. Mario Forni & Domenico Giannone & Marco Lippi & Lucrezia Reichlin, 2008. "Opening the Black Box: Structural Factor Models with Large Cross-Sections," Working Papers ECARES 2008_036, ULB -- Universite Libre de Bruxelles.
  2. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2008. "Nowcasting: The real-time informational content of macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 665-676, May.
  3. Lucrezia Reichlin & Domenico Giannone & Luca Sala, . "Monetary policy in real time," ULB Institutional Repository 2013/10177, ULB -- Universite Libre de Bruxelles.
    • 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.
  4. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  5. D'Agostino, Antonello & Giannone, Domenico, 2007. "Comparing Alternative Predictors Based on Large-Panel Factor Models," CEPR Discussion Papers 6564, C.E.P.R. Discussion Papers.
  6. Gary Koop & Simon Potter, 2003. "Forecasting in large macroeconomic panels using Bayesian Model Averaging," Staff Reports 163, Federal Reserve Bank of New York.
  7. D’Agostino, Antonello & Giannone, Domenico & Surico, Paolo, 2006. "(Un)Predictability and macroeconomic stability," Working Paper Series 0605, European Central Bank.
  8. Jonathan H. Wright, 2009. "Forecasting US inflation by Bayesian model averaging," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 131-144.
  9. 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.
  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. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
  12. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2005. "The generalised dynamic factor model: one sided estimation and forecasting," ULB Institutional Repository 2013/10129, ULB -- Universite Libre de Bruxelles.
  13. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  14. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  15. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  16. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
  17. 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.
  18. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  19. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  20. 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.
  21. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  22. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, 07.
  23. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
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