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Martingale approximation for common factor representation

Author

Listed:
  • 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. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    2. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(02), pages 179-191, August.
    3. Magnus, J.R., 1985. "On differentiating eigenvalues and eigenvectors," Other publications TiSEM f410e3a5-ba9b-4787-b8cc-4, Tilburg University, School of Economics and Management.
    4. 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)

    More about this item

    Keywords

    martingale approximation; dynamic factor model; eigenvalue; stability;

    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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