Determining the Number of Factors in Approximate Factor Models
In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors ("r"), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of "r". We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections ("N") and large time dimensions ("T"). No restriction is imposed on the relation between "N" and "T". Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice. Copyright The Econometric Society 2001.
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.
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.
Volume (Year): 70 (2002)
Issue (Month): 1 (January)
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/Email:
More information through EDIRC
|Order Information:|| Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email: |
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.:
- Allan W. Gregory & Allen C. Head, 1996.
"Common and Country-specific Fluctuations in Productivity, Investment, and the Current Account,"
931, Queen's University, Department of Economics.
- Gregory, Allan W. & Head, Allen C., 1999. "Common and country-specific fluctuations in productivity, investment, and the current account," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 423-451, December.
- John H. Cochrane, 1999.
"New Facts in Finance,"
NBER Working Papers
7169, National Bureau of Economic Research, Inc.
- James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
- David Backus & Silverio Foresi & Abon Mozumdar & Liuren Wu, 1998.
"Predictable Changes in Yields and Forward Rates,"
NBER Working Papers
6379, National Bureau of Economic Research, Inc.
- Mario Forni & Lucrezia Reichlin, 1998.
"Let's get real: a factor analytical approach to disaggregated business cycle dynamics,"
ULB Institutional Repository
2013/10147, ULB -- Universite Libre de Bruxelles.
- Forni, Mario & Reichlin, Lucrezia, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 453-73, July.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- Forni, Mario & Lippi, Marco, 2000.
"The Generalized Dynamic Factor Model: Representation Theory,"
CEPR Discussion Papers
2509, C.E.P.R. Discussion Papers.
- Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
- Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000.
"The generalised dynamic factor model: identification and estimation,"
ULB Institutional Repository
2013/10143, ULB -- Universite Libre de Bruxelles.
- 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.
- 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.
- Thomas J. Sargent & Christopher A. Sims, 1977.
"Business cycle modeling without pretending to have too much a priori economic theory,"
55, Federal Reserve Bank of Minneapolis.
- Tom Doan, . "RATS program to estimate observable index model from Sargent-Sims(1977)," Statistical Software Components RTZ00126, Boston College Department of Economics.
- Schwert, G William, 1989.
"Tests for Unit Roots: A Monte Carlo Investigation,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 7(2), pages 147-59, April.
- Stock, James H. & Watson, Mark W., 1999.
Journal of Monetary Economics,
Elsevier, vol. 44(2), pages 293-335, October.
- Ghysels, E. & Ng, S., 1996.
"A Semi-Parametric Factor Model for Interest Rates,"
Cahiers de recherche
9612, Universite de Montreal, Departement de sciences economiques.
- Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Eric Ghysels & Serena Ng, 1996. "A Semi-Parametric Factor Model for Interest Rates," CIRANO Working Papers 96s-18, CIRANO.
- Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2000. "Reference Cycles: The NBER Methodology Revisited," CEPR Discussion Papers 2400, C.E.P.R. Discussion Papers.
- Geweke, John F & Meese, Richard, 1981.
"Estimating Regression Models of Finite but Unknown Order,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 55-70, February.
- Geweke, John & Meese, Richard, 1981. "Estimating regression models of finite but unknown order," Journal of Econometrics, Elsevier, vol. 16(1), pages 162-162, May.
- Stock, J.H. & Watson, M.W., 1989.
"New Indexes Of Coincident And Leading Economic Indicators,"
178d, Harvard - J.F. Kennedy School of Government.
- 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.
- 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.
- 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.
- Allan W. Gregory & Allen C. Head & Jacques Raynauld, 1994.
"Measuring World Business Cycles,"
902, Queen's University, Department of Economics.
- Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
- 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.
- Forni, Mario & Lippi, Marco, 1997. "Aggregation and the Microfoundations of Dynamic Macroeconomics," OUP Catalogue, Oxford University Press, number 9780198288008.
- Dhrymes, Phoebus J & Friend, Irwin & Gultekin, N Bulent, 1984. " A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 39(2), pages 323-46, June.
- Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:70:y:2002:i:1:p:191-221. 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: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
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.