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Martingale approximation of eigenvalues for common factor representation

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  • Bystrov, Victor
  • di Salvatore, Antonietta

Abstract

In this paper a martingale approximation is used to derive an asymptotic distribution of simple positive eigenvalues of the sample covariance matrix for a stationary process. The derived distribution can be used to study stability of the common factor representation based on the principal component analysis of the covariance matrix.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 83 (2013)
Issue (Month): 1 ()
Pages: 233-237

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Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:233-237

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Related research

Keywords: Martingale approximation; Dynamic factor model; Eigenvalue; Stability;

References

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  1. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2008. "Forecasting Macroeconomic Variables Using Diffusion Indexes in Short Samples with Structural Change," Working Papers 334, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  2. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(02), pages 179-191, August.
  3. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  4. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, 09.
  5. Magnus, J.R., 1985. "On differentiating eigenvalues and eigenvectors," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153213, Tilburg University.
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