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Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?

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

Abstract

This paper considers Bayesian regression with normal and double exponential 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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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5829.

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Date of creation: Sep 2006
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Handle: RePEc:cpr:ceprdp:5829

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Keywords: Bayesian VAR; large cross-sections; Lasso regression; principal components; ridge regressions;

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References

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  1. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
  7. Antonello D'Agostino & Domenico Giannone & Paolo Surico, 2005. "(Un)Predictability and Macroeconomic Stability," Macroeconomics 0510024, EconWPA.
  8. Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 31 Jul 1999.
  9. Jonathan H. Wright, 2003. "Forecasting U.S. inflation by Bayesian Model Averaging," International Finance Discussion Papers 780, Board of Governors of the Federal Reserve System (U.S.).
  10. Domenico Giannone & Lucrezia Reichlin & David Small, 2005. "Nowcasting GDP and inflation: the real-time informational content of macroeconomic data releases," Finance and Economics Discussion Series 2005-42, Board of Governors of the Federal Reserve System (U.S.).
  11. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2004. "The generalised dynamic factor model: consistency and rates," ULB Institutional Repository 2013/10133, ULB -- Universite Libre de Bruxelles.
  12. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
  13. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  14. 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.
  15. 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.
  16. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
  17. D’Agostino, Antonello & Giannone, Domenico, 2006. "Comparing alternative predictors based on large-panel factor models," Working Paper Series 0680, European Central Bank.
  18. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  19. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  20. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  21. 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.
  22. 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.
  23. Gary Koop & Simon Potter, 2003. "Forecasting in Large Macroeconomic Panels using Bayesian Model Averaging," Discussion Papers in Economics 04/16, Department of Economics, University of Leicester.
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