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A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering

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  • Doz, Catherine
  • Giannone, Domenico
  • Reichlin, Lucrezia

Abstract

This paper shows consistency of a two step estimator of the parameters of a dynamic approximate factor model when the panel of time series is large (n large). In the first step, the parameters are first estimated from an OLS on principal components. In the second step, the factors are estimated via the Kalman smoother. This projection allows to consider dynamics in the factors and heteroskedasticity in the idiosyncratic variance. The analysis provides theoretical backing for the estimator considered in Giannone, Reichlin, and Sala (2004) and Giannone, Reichlin, and Small (2005).

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6043.

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Date of creation: Jan 2007
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Handle: RePEc:cpr:ceprdp:6043

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Keywords: Factor Models; Kalman filter; large cross-sections; principal components;

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References

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  1. Karim Barhoumi & Szilard Benk & Riccardo Cristadoro & Ard Den Reijer & Audrone Jakaitiene & Piotr Jelonek & António Rua & Gerhard Rünstler & Karsten Ruth & Christophe Van Nieuwenhuyze, 2008. "Short-term forecasting of GDP using large monthly datasets - a pseudo real-time forecast evaluation exercise," Occasional Paper Series 84, European Central Bank.
  2. 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.
  3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  4. 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.
  5. Bańbura, Marta & Rünstler, Gerhard, 2011. "A look into the factor model black box: Publication lags and the role of hard and soft data in forecasting GDP," International Journal of Forecasting, Elsevier, vol. 27(2), pages 333-346.
  6. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2005. "Nowcasting GDP and Inflation: The Real Time Informational Content of Macroeconomic Data Releases," CEPR Discussion Papers 5178, C.E.P.R. Discussion Papers.
  7. Elena Angelini & Gonzalo Camba‐Mendez & Domenico Giannone & Lucrezia Reichlin & Gerhard Rünstler, 2011. "Short‐term forecasts of euro area GDP growth," Econometrics Journal, Royal Economic Society, vol. 14(1), pages C25-C44, February.
  8. 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.
  9. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2002. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," CEPR Discussion Papers 3432, C.E.P.R. Discussion Papers.
  10. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2006. "A Two-step estimator for large approximate dynamic factor models based on Kalman filtering," THEMA Working Papers 2006-23, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  11. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2010. "Are disaggregate data useful for factor analysis in forecasting French GDP?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 132-144.
  12. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
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  14. Mario Forni & Lucrezia Reichlin, 2001. "Federal policies and local economies: Europe and the U.S," ULB Institutional Repository 2013/10141, ULB -- Universite Libre de Bruxelles.
  15. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  16. Antonello D’ Agostino & Domenico Giannone, 2012. "Comparing Alternative Predictors Based on Large‐Panel Factor Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 306-326, 04.
  17. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  18. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  19. Boriss Siliverstovs & Konstantin A. Kholodilin, 2010. "Assessing the Real-Time Informational Content of Macroeconomic Data Releases for Now-/Forecasting GDP: Evidence for Switzerland," Discussion Papers of DIW Berlin 970, DIW Berlin, German Institute for Economic Research.
  20. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "A quasi maximum likelihood approach for large approximate dynamic factor models," Working Paper Series 0674, European Central Bank.
  21. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," CEP Discussion Papers dp0132, Centre for Economic Performance, LSE.
  22. 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.
  23. 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.
  24. Troy Matheson, 2007. "An analysis of the informational content of New Zealand data releases: the importance of business opinion surveys," Reserve Bank of New Zealand Discussion Paper Series DP2007/13, Reserve Bank of New Zealand.
  25. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  26. 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.
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