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Efficient Estimation Of Factor Models

  • Choi, In
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This paper considers the factor model Xt = Ft + et. Assuming a nor- mal distribution for the idiosyncratic error et conditional on the factors fFtg, conditional maximum likelihood estimators of the factor and factor- loading spaces are derived. These estimators are called generalized prin- cipal component estimators (GPCEs) without the normality assumption. This paper derives the asymptotic distributions of the GPCEs of the fac- tor and factor-loading space. It is shown that variances of the GPCEs of the common components are smaller than those of the principal com- ponent estimators studied in Bai (2003). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component es- timators. The feasible GPCE (FGPCE) of factor space is shown to be asymptotically equivalent to the GPCE. The GPCEs and FGPCEs are shown to be more efficient than the principal component estimators in finite samples.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 28 (2012)
Issue (Month): 02 (April)
Pages: 274-308

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Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:274-308_00
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  1. Massimiliano Marcellino & Carlo A. Favero & Francesca Neglia, 2005. "Principal components at work: the empirical analysis of monetary policy with large data sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 603-620.
  2. 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.
  3. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2003. "The Generalized Dynamic Factor Model. One-Sided Estimation and Forecasting," LEM Papers Series 2003/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  4. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  6. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 217-259, 06.
  7. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2003. "Do financial variables help forecasting inflation and real activity in the euro area?," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1243-1255, September.
  8. 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.
  9. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  10. 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.
  11. Jones, Christopher S., 2001. "Extracting factors from heteroskedastic asset returns," Journal of Financial Economics, Elsevier, vol. 62(2), pages 293-325, November.
  12. Jushan Bai & Serena Ng, 2001. "A PANIC Attack on Unit Roots and Cointegration," Boston College Working Papers in Economics 519, Boston College Department of Economics.
  13. MOON, Hyungsik Roger & PERRON, Benoit., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche 2002-18, Universite de Montreal, Departement de sciences economiques.
  14. 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.
  15. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
  16. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1577-1606, December.
  17. George Kapetanios & Massimiliano Marcellino, 2009. "A parametric estimation method for dynamic factor models of large dimensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 208-238, 03.
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