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A Robust Criterion for Determining the Number of Factors in Approximate Factor Models

  • Lucia Alessi
  • Matteo Barigozzi
  • Marco Capasso

We modify the criterion by Bai and Ng (2002) for determining the number of factors in approximate factor models. As in the original criterion, for any given number of factors we estimate the common and idiosyncratic components of the model by applying principal component analysis. We select the true number of factors as the number that minimizes the variance explained by the idiosyncratic component. In order to avoid overparametrization, minimization is subject to penalization. At this step, we modify the original procedure by multiplying the penalty function by a positive real number, which allows us to tune its penalizing power, by analogy with the method used by Hallin and Liška (2007) in the frequency domain. The contribution of this paper is twofold. First, our criterion retains the asymptotic properties of the original criterion, but corrects its tendency to overestimate the true number of factors. Second, we provide a computationally easy way to implement the new method by iteratively applying the original criterion. Monte Carlo simulations show that our criterion is in general more robust than the original one. A better performance is achieved in particular in the case of large idiosyncratic disturbances. These conditions are the most difficult for detecting a factor structure but are not unusual in the empirical context. Two applications on a macroeconomic and a financial dataset are also presented.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2009_023.

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Length: 21 p.
Date of creation: 2009
Date of revision:
Publication status: Published by:
Handle: RePEc:eca:wpaper:2009_023
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  1. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  2. Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2006. "VARs, common factors and the empirical validation of equilibrium business cycle models," ULB Institutional Repository 2013/10127, ULB -- Universite Libre de Bruxelles.
  3. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  4. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
  5. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2007. "Opening the black box: structural factor models with large cross-sections," Working Paper Series 0712, European Central Bank.
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  7. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
  8. 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.
  9. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  10. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
  11. Filippo Altissimo & Riccardo Cristadoro & Mario Forni & Marco Lippi & Giovanni Veronese, 2010. "New Eurocoin: Tracking Economic Growth in Real Time," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1024-1034, November.
  12. Mario Forno & Marco Lippi & Lucrezia Reichlin & Filippo Altissimo & Antonio Bassanetti, 2003. "Eurocoin: A Real Time Coincident Indicator Of The Euro Area Business Cycle," Computing in Economics and Finance 2003 242, Society for Computational Economics.
  13. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  14. 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.
  15. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
  16. Ben S. Bernanke & Jean Boivin, 2001. "Monetary Policy in a Data-Rich Environment," NBER Working Papers 8379, National Bureau of Economic Research, Inc.
  17. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
  18. 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.
  19. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, 05.
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