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Determining the number of factors from empirical distribution of eigenvalues

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Author Info
Alexei Onatski () (Columbia University - Department of Economics)

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Abstract

We develop a new consistent and simple to compute estimator of the number of factors in the approximate factor models of Chamberlain and Rothchild (1983). Our setting requires both time series and cross-sectional dimensions of the data to be large. The main theoretical advantage of our estimator relative to the previously proposed ones is that it works well even in the situation when the portion of the observed variance attributed to the factors is small relative to the variance due to the idiosyncratic term. This advantage arises because the estimator is based on a Law-of-Large- Numbers type regularity for the idiosyncratic components of the data, as opposed to the estimators based on the assumption that a significant portion of the variance is explained by the systematic part. Extensive Monte Carlo analysis shows that our estimator outperforms the recently proposed Bai and Ng (2002) estimators in finite samples when the ignal-to-noise” ratio is relatively small. We apply the new estimation procedure to determine the number of pervasive factors driving stock returns for the companies traded on NYSE, AMEX, and NASDAQ in the period from 1983 to 2003. Our estimate is equal to 8.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0405-19.

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Length: 29 pages
Date of creation: 2005
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Handle: RePEc:clu:wpaper:0405-19

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  1. Forni, Mario & Reichlin, Lucrezia, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 453-73, July. [Downloadable!] (restricted)
  2. Forni, Mario & Lippi, Marco, 1999. "Aggregation of linear dynamic microeconomic models," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 131-158, February. [Downloadable!] (restricted)
  3. Trzcinka, Charles A, 1986. " On the Number of Factors in the Arbitrage Pricing Model," Journal of Finance, American Finance Association, vol. 41(2), pages 347-68, June. [Downloadable!] (restricted)
  4. Reinganum, Marc R, 1981. "The Arbitrage Pricing Theory: Some Empirical Results," Journal of Finance, American Finance Association, vol. 36(2), pages 313-21, May. [Downloadable!] (restricted)
  5. Brown, Stephen J & Weinstein, Mark I, 1983. " A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm," Journal of Finance, American Finance Association, vol. 38(3), pages 711-43, June. [Downloadable!] (restricted)
  6. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January. [Downloadable!] (restricted)
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  10. Silverstein, J. W. & Choi, S. I., 1995. "Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 295-309, August. [Downloadable!] (restricted)
  11. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2004. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," NBER Working Papers 10220, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Huang, Roger D. & Jo, Hoje, 1995. "Data frequency and the number of factors in stock returns," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 987-1003, September. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. Roll, Richard & Ross, Stephen A, 1980. " An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December. [Downloadable!] (restricted)
  15. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December. [Downloadable!] (restricted)
  16. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August. [Downloadable!] (restricted)
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  1. Qin, Duo, 2007. "Uncover Latent PPP by Dynamic Factor Error Correction Model (DF-ECM) Approach: Evidence from five OECD countries," Economics Discussion Papers 2007-29, Kiel Institute for the World Economy. [Downloadable!]
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  2. Chihwa Kao & Lorenzo Trapani & Giovanni Urga, 2006. "The Asymptotics for Panel Models with Common Shocks," Center for Policy Research Working Papers 77, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  3. Martin Wagner, 2008. "On PPP, unit roots and panels," Empirical Economics, Springer, vol. 35(2), pages 229-249, September. [Downloadable!] (restricted)
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  4. Holly, S. & Petrella, I., 2008. "Factor demand linkages and the business cycle: Interpreting aggregate fluctuations as sectoral fluctuations," Cambridge Working Papers in Economics 0827, Faculty of Economics, University of Cambridge. [Downloadable!]
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