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Asymptotics of the principal components estimator of large factor models with weakly influential factors

  • Onatski, Alexei

This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose an estimator of the number of factors for which the PC estimator works reasonably well. For the special case when the idiosyncratic terms are cross-sectionally but not temporally correlated (or vice versa), we show that the coefficients in the OLS regressions of the PC estimates of factors (loadings) on the true factors (true loadings) are asymptotically normal, and find explicit formulae for the corresponding asymptotic covariance matrix. We explain how to estimate the parameters of the derived asymptotic distributions. Our Monte Carlo analysis suggests that our asymptotic formulae and estimators work well even for relatively small n and T. We apply our theoretical results to test a hypothesis about the factor content of the US stock return data.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 2 ()
Pages: 244-258

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Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:244-258
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  17. McManus, Douglas A., 1991. "Who Invented Local Power Analysis?," Econometric Theory, Cambridge University Press, vol. 7(02), pages 265-268, June.
  18. Lucrezia Reichlin, 2003. "Factor models in large cross sections of time series," ULB Institutional Repository 2013/10179, ULB -- Universite Libre de Bruxelles.
  19. Forni, Mario & Lippi, Marco, 1999. "Aggregation of linear dynamic microeconomic models," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 131-158, February.
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