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A quasi maximum likelihood approach for large approximate dynamic factor models

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

This paper considers quasi-maximum likelihood estimations of a dynamic approximate factor model when the panel of time series is large. Maximum likelihood is analyzed under different sources of misspecification: omitted serial correlation of the observations and cross-sectional correlation of the idiosyncratic components. It is shown that the effects of misspecification on the estimation of the common factors is negligible for large sample size (T) and the cross sectional dimension (n). The estimator is feasible when n is large and easily implementable using the Kalman smoother and the EM algorithm as in traditional factor analysis. Simulation results illustrate what are the empirical conditions in which we can expect improvement with respect to simple principle components considered by Bai (2003), Bai and Ng (2002), Forni, Hallin, Lippi, and Reichlin (2000, 2005b), Stock and Watson (2002a,b). JEL Classification: C51, C32, C33

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Paper provided by European Central Bank in its series Working Paper Series with number 0674.

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Date of creation: Sep 2006
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Handle: RePEc:ecb:ecbwps:20060674
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  1. James H. Stock & Mark W. Watson, 1988. "A Probability Model of The Coincident Economic Indicators," NBER Working Papers 2772, National Bureau of Economic Research, Inc.
  2. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2007. "A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering," CEPR Discussion Papers 6043, C.E.P.R. Discussion Papers.
  3. 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.
  4. 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.
  5. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," NBER Chapters, in: Business Cycles, Indicators and Forecasting, pages 285-310 National Bureau of Economic Research, Inc.
  6. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  7. 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.
  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. Giannone, Domenico & Reichlin, Lucrezia & Sala, Luca, 2005. "Monetary Policy in Real Time," CEPR Discussion Papers 4981, C.E.P.R. Discussion Papers.
    • 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.
  10. Marta Bańbura & Michele Modugno, 2014. "Maximum Likelihood Estimation Of Factor Models On Datasets With Arbitrary Pattern Of Missing Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 133-160, 01.
  11. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409 National Bureau of Economic Research, Inc.
  12. Ricardo Reis & Mark W. Watson, 2007. "Relative Goods' Prices, Pure Inflation, and the Phillips Correlation," NBER Working Papers 13615, National Bureau of Economic Research, Inc.
  13. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1319-1347, October.
  14. Gregory Connor and Robert Korajczyk., 1987. "Risk and Return in an Equilibrium APT," Research Program in Finance Working Papers 174, University of California at Berkeley.
  15. Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-91, September.
  16. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
  17. Domenico Giannone & Lucrezia Reichlin & David H. 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.).
  18. repec:hal:journl:peer-00844811 is not listed on IDEAS
  19. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
  20. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
  21. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
  22. Forni, Mario & Reichlin, Lucrezia, 2001. "Federal policies and local economies: Europe and the US," European Economic Review, Elsevier, vol. 45(1), pages 109-134, January.
  23. 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.
  24. 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.
  25. M. Ayhan Kose & Christopher Otrok & Charles H. Whiteman, 2003. "International Business Cycles: World, Region, and Country-Specific Factors," American Economic Review, American Economic Association, vol. 93(4), pages 1216-1239, September.
  26. repec:adr:anecst:y:1999:i:54:p:05 is not listed on IDEAS
  27. Sentana, E. & Shah, M., 1994. "An Index of Co-Movements in Financial Time Series," Papers 9415, Centro de Estudios Monetarios Y Financieros-.
  28. Reis, Ricardo & Watson, Mark W, 2007. "Relative Goods’ Prices and Pure Inflation," CEPR Discussion Papers 6593, C.E.P.R. Discussion Papers.
  29. 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.
  30. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  31. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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