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Martingale approximation for common factor representation

Author

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  • Bystrov, Victor
  • di Salvatore, Antonietta

Abstract

In this paper a martingale approximation is used to derive the limiting distribution of simple positive eigenvalues of the sample covariance matrix for a stationary linear 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.

Suggested Citation

  • Bystrov, Victor & di Salvatore, Antonietta, 2012. "Martingale approximation for common factor representation," MPRA Paper 37669, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37669
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    File URL: https://mpra.ub.uni-muenchen.de/39840/1/MPRA_paper_39840.pdf
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    References listed on IDEAS

    as
    1. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    2. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    3. Castle, Jennifer & Shephard, Neil (ed.), 2009. "The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry," OUP Catalogue, Oxford University Press, number 9780199237197.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    martingale approximation; dynamic factor model; eigenvalue; stability;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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