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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
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Handle: RePEc:eca:wpaper:2009_023
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  1. Mario Forni & Filippo Altissimo & Riccardo Cristadoro & Marco Lippi & Giovanni Veronese., 2008. "New Eurocoin: Tracking Economic Growth in Real Time," Center for Economic Research (RECent) 020, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
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  11. 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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  14. 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.
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  16. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
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