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Maximum likelihood estimation and inference for approximate factor models of high dimension

  • Bai, Jushan
  • Li, Kunpeng

An approximate factor model of high dimension has two key features. First, the idiosyncratic errors are correlated and heteroskedastic over both the cross-section and time dimensions; the correlations and heteroskedasticities are of unknown forms. Second, the number of variables is comparable or even greater than the sample size. Thus a large number of parameters exist under a high dimensional approximate factor model. Most widely used approaches to estimation are principal component based. This paper considers the maximum likelihood-based estimation of the model. Consistency, rate of convergence, and limiting distributions are obtained under various identification restrictions. Comparison with the principal component method is made. The likelihood-based estimators are more efficient than those of principal component based. Monte Carlo simulations show the method is easy to implement and an application to the U.S. yield curves is considered

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File URL: https://mpra.ub.uni-muenchen.de/42118/2/MPRA_paper_42118.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42099.

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Date of creation: 10 Jan 2012
Date of revision: 19 Oct 2012
Handle: RePEc:pra:mprapa:42099
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  1. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
  2. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
  3. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
  4. 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.
  5. Catherine Doz & Lucrezia Reichlin, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Post-Print peer-00844811, HAL.
  6. 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.
  7. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  8. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
  9. Xu Han & Atsushi Inoue, 2011. "Tests for Parameter Instability in Dynamic Factor Models," TERG Discussion Papers 306, Graduate School of Economics and Management, Tohoku University, revised May 2013.
  10. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  11. Breitung, Jörg & Tenhofen, Jörn, 2011. "GLS Estimation of Dynamic Factor Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1150-1166.
  12. 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.
  13. 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.
  14. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
  15. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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