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

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  • Bai, Jushan
  • Li, Kunpeng

Abstract

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

Suggested Citation

  • Bai, Jushan & Li, Kunpeng, 2012. "Maximum likelihood estimation and inference for approximate factor models of high dimension," MPRA Paper 42099, University Library of Munich, Germany, revised 19 Oct 2012.
  • Handle: RePEc:pra:mprapa:42099
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    References listed on IDEAS

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    1. 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.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    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. 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.
    5. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    6. 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.
    7. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    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. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1117-1152, October.
    10. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    11. 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.
    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. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    14. 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.
    15. 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.
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    Citations

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    Cited by:

    1. Helmut Lütkepohl, 2014. "Structural Vector Autoregressive Analysis in a Data Rich Environment: A Survey," SFB 649 Discussion Papers SFB649DP2014-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. repec:eee:jmvana:v:158:y:2017:i:c:p:73-86 is not listed on IDEAS
    3. Li, Kunpeng & Li, Qi & Lu, Lina, 2016. "Quasi Maximum Likelihood Analysis of High Dimensional Constrained Factor Models," MPRA Paper 75676, University Library of Munich, Germany.
    4. Jushan Bai & Kunpeng Li & Lina Lu, 2016. "Estimation and Inference of FAVAR Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 620-641, October.
    5. Li, Kunpeng & Lu, Lina, 2014. "Efficient estimation of heterogeneous coefficients in panel data models with common shock," MPRA Paper 59312, University Library of Munich, Germany.
    6. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.

    More about this item

    Keywords

    Factor analysis; Approximate factor models; Maximum likelihood; Kalman smoother; Principal components; Inferential theory;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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