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Dynamic Factor Models with Infinite-Dimensional Factor Space: One-Sided Representations

  • Mario Forni
  • Marc Hallin
  • Marco Lippi
  • Paolo Zaffaroni

Abstract. Factor model methods recently have become extremely popular in the theory andpractice of large panels of time series data. Those methods rely on various factor models whichall are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced inForni, Hallin, Lippi and Reichlin (2000). That paper, however, relies on Brillinger's dynamicprincipal components. The corresponding estimators are two-sided filters whose performanceat the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have beendominant in this literature. On the other hand, those estimators require the assumptionthat the space spanned by the factors has finite dimension. In the present paper, we arguethat such an assumption is extremely restrictive and potentially quite harmful. Elaboratingupon recent results by Anderson and Deistler (2008a, b) on singular stationary processes withrational spectrum, we obtain one-sided representations for the GDFM without assuming finitedimension of the factor space. Construction of the corresponding estimators is also brieflyoutlined. In a companion paper, we establish consistency and rates for such estimators, andprovide Monte Carlo results further motivating our approach.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2012-046.

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Length: 40 p.
Date of creation: Dec 2012
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Handle: RePEc:eca:wpaper:2013/134458
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  1. Mario Forni & Filippo Altissimo & Riccardo Cristadoro & Marco Lippi & Giovanni Veronese., 2008. "New Eurocoin: Tracking Economic Growth in Real Time," Center for Economic Research (RECent) 020, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
  2. 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.
  3. 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.
  4. 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.
  5. repec:ulb:ulbeco:2013/136188 is not listed on IDEAS
  6. Corielli, Francesco & Marcellino, Massimiliano, 2006. "Factor based index tracking," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2215-2233, August.
  7. 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.
  8. 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.
  9. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," CEP Discussion Papers dp0132, Centre for Economic Performance, LSE.
  10. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
  11. 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.
  12. Boivin, Jean & Giannoni, Marc P. & Mihov, Ilian, 2006. "Sticky prices and monetary policy: Evidence from disaggregated US data," CFS Working Paper Series 2007/14, Center for Financial Studies (CFS).
  13. Marc Hallin & Charles Mathias & Hugues Pirotte & David Veredas, 2011. "Market liquidity as dynamic factors," Working Papers ECARES 163, 42-50, ULB -- Universite Libre de Bruxelles.
  14. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  15. Eickmeier, Sandra, 2007. "Business cycle transmission from the US to Germany--A structural factor approach," European Economic Review, Elsevier, vol. 51(3), pages 521-551, April.
  16. Sydeny C. Ludvigson & Serena Ng, 2005. "Macro Factors in Bond Risk Premia," NBER Working Papers 11703, National Bureau of Economic Research, Inc.
  17. 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.
  18. 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".
  19. 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.
  20. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  21. 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.
  22. Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary policy in real time," ULB Institutional Repository 2013/6401, 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.
  23. Mario Forni & Marc Hallin & Marco Lippi & Paolo Zaffaroni, 2011. "One-Sided Representations of Generalized Dynamic Factor Models," DSS Empirical Economics and Econometrics Working Papers Series 2011/5, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
  24. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
  25. 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.
  26. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, 09.
  27. 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.
  28. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. Bernanke, Ben S. & Boivin, Jean, 2003. "Monetary policy in a data-rich environment," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 525-546, April.
  34. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  35. 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.
  36. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  37. 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.
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