Advanced Search
MyIDEAS: Login to save this article or follow this journal

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

Contents:

Author Info

  • Onatski, Alexei

Abstract

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/pii/S0304407612000449
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

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

as in new window
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

Related research

Keywords: Approximate factor models; Principal components; Weakly influential factors; Weak factors; Inconsistency; Bias; Asymptotic distribution; Marchenko–Pastur law;

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Jean Boivin & Marc P. Giannoni & Benoît Mojon, 2008. "How Has the Euro Changed the Monetary Transmission?," NBER Working Papers 14190, National Bureau of Economic Research, Inc.
  2. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  3. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
  4. 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.
  5. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  6. Gregory Connor & Oliver Linton, 2006. "Semiparametric estimation of a characteristic-based factor model of common stock returns," LSE Research Online Documents on Economics 4424, London School of Economics and Political Science, LSE Library.
  7. Alexei Onatski, 2005. "Determining the number of factors from empirical distribution of eigenvalues," Discussion Papers, Columbia University, Department of Economics 0405-19, Columbia University, Department of Economics.
  8. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "A quasi maximum likelihood approach for large approximate dynamic factor models," Working Paper Series 0674, European Central Bank.
  9. 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.
  10. Reichlin, Lucrezia, 2002. "Factor Models in Large Cross-Sections of Time Series," CEPR Discussion Papers 3285, C.E.P.R. Discussion Papers.
  11. Christine De Mol & Domenico Giannone & Lucrezia Reichlin, 2008. "Forecasting using a large number of predictors: is Bayesian shrinkage a valid alternative to principal components?," ULB Institutional Repository 2013/6411, ULB -- Universite Libre de Bruxelles.
  12. Forni, Mario & Lippi, Marco, 1999. "Aggregation of linear dynamic microeconomic models," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 131-158, February.
  13. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  14. 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.
  15. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 135-171, January.
  16. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, Elsevier, vol. 132(1), pages 169-194, May.
  17. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2011. "Asymptotic Power of Sphericity Tests for High-Dimensional Data," Working Papers ECARES ECARES 2011-018, ULB -- Universite Libre de Bruxelles.
  18. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(2), pages 147-62, April.
  19. McManus, Douglas A., 1991. "Who Invented Local Power Analysis?," Econometric Theory, Cambridge University Press, vol. 7(02), pages 265-268, June.
  20. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, Elsevier, vol. 33(1), pages 3-56, February.
  21. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, Econometric Society, vol. 62(3), pages 657-81, May.
  22. Carhart, Mark M, 1997. " On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
  23. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, now publishers, vol. 3(2), pages 89-163, June.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Gobillon, Laurent & Magnac, Thierry, 2013. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," IZA Discussion Papers 7493, Institute for the Study of Labor (IZA).
  2. Luciani, Matteo, 2014. "Forecasting with approximate dynamic factor models: The role of non-pervasive shocks," International Journal of Forecasting, Elsevier, Elsevier, vol. 30(1), pages 20-29.
  3. Alj, Abdelkamel & Azrak, Rajae & Mélard, Guy, 2014. "On conditions in central limit theorems for martingale difference arrays," Economics Letters, Elsevier, vol. 123(3), pages 305-307.
  4. Reijer, Ard H.J. de & Jacobs, Jan P.A.M. & Otter, Pieter W., 2014. "A criterion for the number of factors in a data-rich environment," Research Report 14008-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  5. repec:hal:wpaper:halshs-00849071 is not listed on IDEAS
  6. Xu Cheng & Bruce E. Hansen, 2012. "Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach," PIER Working Paper Archive 12-046, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:168:y:2012:i:2:p:244-258. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.