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One-Sided Representations of Generalized Dynamic Factor Models

  • Mario Forni

    (Università di Modena e Reggio Emilia, CEPR and RECent)

  • Marc Hallin

    (ECARES, Université Libre de Bruxelles and ORFE, Princeton University)

  • Marco Lippi

    (Università di Roma "La Sapienza" and EIEF)

  • Paolo Zaffaroni

    (Imperial College London and Università di Roma "La Sapienza")

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000). In that paper, however, estimation relies on Brillinger’s concept of dynamic principal components, which produces filters that are in general two-sided and therefore yield poor performances at the end of the observation period and hardly can be used for forecasting purposes. In the present paper, we remedy this problem, and show how, based on recent results on singular stationary processes with rational spectra, one-sided estimators are possible for the parameters and the common shocks in the GDFM. Consistency is obtained, along with rates. An empirical section, based on US macroeconomic time series, compares estimates based on our model with those based on the usual staticrepresentation restriction, and provide convincing evidence that the assumptions underlying the latter are not supported by the data.

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Paper provided by Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome in its series DSS Empirical Economics and Econometrics Working Papers Series with number 2011/5.

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Length: 62 pages
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:sas:wpaper:20115
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  1. Giannone, Domenico & Reichlin, Lucrezia & Small, David H., 2006. "Nowcasting GDP and inflation: the real-time informational content of macroeconomic data releases," Working Paper Series 0633, European Central Bank.
  2. Mario Forni & Luca Gambetti, 2008. "The dynamic e ects of monetary policy: A structural factor model approach," Center for Economic Research (RECent) 026, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
  3. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  4. Boivin, Jean & Giannoni, Marc & Mihov, Ilian, 2007. "Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data," CEPR Discussion Papers 6101, C.E.P.R. Discussion Papers.
  5. Eickmeier, Sandra, 2004. "Business Cycle Transmission from the US to Germany: a Structural Factor Approach," Discussion Paper Series 1: Economic Studies 2004,12, Deutsche Bundesbank, Research Centre.
  6. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  7. Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000. "The generalised dynamic factor model: identification and estimation," ULB Institutional Repository 2013/10143, ULB -- Universite Libre de Bruxelles.
  8. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1997. "Monetary policy shocks: what have we learned and to what end?," Working Paper Series, Macroeconomic Issues WP-97-18, Federal Reserve Bank of Chicago.
  9. Francesco Corielli & Massimiliano Marcellino, . "Factor Based Index Trading," Working Papers 209, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  10. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  11. 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.
  12. Carlo Ambrogio Favero & Massimilano Marcellino & Francesca Neglia, . "Principal components at work: The empirical analysis of monetary policy with large datasets," Working Papers 223, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  13. 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.
  14. Mario Forni & Domenico Giannone & Marco Lippi & Lucrezia Reichlin, 2007. "Opening the Black Box: Structural Factor Models with Large Cross-Sections," Center for Economic Research (RECent) 008, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
  15. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, July.
  16. 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.
  17. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
  18. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
  19. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
  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. Forni, Mario & Gambetti, Luca, 2010. "Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model," CEPR Discussion Papers 7692, C.E.P.R. Discussion Papers.
  22. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
  23. Altissimo, Filippo & Cristadoro, Riccardo & Forni, Mario & Lippi, Marco & Veronese, Giovanni, 2006. "New EuroCOIN: Tracking Economic Growth in Real Time," CEPR Discussion Papers 5633, C.E.P.R. Discussion Papers.
  24. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  25. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2004. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," NBER Working Papers 10220, National Bureau of Economic Research, Inc.
  26. Forni, Mario & Lippi, Marco, 2011. "The general dynamic factor model: One-sided representation results," Journal of Econometrics, Elsevier, vol. 163(1), pages 23-28, July.
  27. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
  28. Ben S. Bernanke & Jean Boivin, 2001. "Monetary Policy in a Data-Rich Environment," NBER Working Papers 8379, National Bureau of Economic Research, Inc.
  29. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  30. Altissimo, Filippo & Mojon, Benoit & Zaffaroni, Paolo, 2009. "Can aggregation explain the persistence of inflation?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 231-241, March.
  31. Cristadoro, Riccardo & Forni, Mario & Reichlin, Lucrezia & Veronese, Giovanni, 2005. "A Core Inflation Indicator for the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 539-60, June.
  32. Hallin, Marc & Mathias, Charles & Pirotte, Hugues & Veredas, David, 2011. "Market liquidity as dynamic factors," Journal of Econometrics, Elsevier, vol. 163(1), pages 42-50, July.
  33. 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.
  34. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
  35. repec:sol:wpaper:10-021 is not listed on IDEAS
  36. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, 09.
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