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Estimation of a Multiplicative Covariance Structure

Author

Listed:
  • Christian M. Hafner

    (Institute for Fiscal Studies)

  • Oliver Linton

    () (Institute for Fiscal Studies and University of Cambridge)

  • Haihan Tang

    (Institute for Fiscal Studies)

Abstract

We consider a Kronecker product structure for large covariance matrices, which has the feature that the number of free parameters increases logarithmically with the dimensions of the matrix. We propose an estimation method of the free parameters based on the log linear property of this structure, and also a Quasi-Likelihood method. We establish the rate of convergence of the estimated parameters when the size of the matrix diverges. We also establish a CLT for our method. We apply the method to portfolio choice for S&P500 daily returns and compare with sample covariance based methods and with the recent Fan et al. (2013) method.

Suggested Citation

  • Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a Multiplicative Covariance Structure," CeMMAP working papers CWP23/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:23/16
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    References listed on IDEAS

    as
    1. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    2. Magnus, Jan R. & Neudecker, H., 1986. "Symmetry, 0-1 Matrices and Jacobians: A Review," Econometric Theory, Cambridge University Press, vol. 2(02), pages 157-190, August.
    3. Magnus, J.R. & Neudecker, H., 1986. "Symmetry, 0-1 matrices and Jacobians : A review," Other publications TiSEM c1c491d0-f2bf-4de1-94f8-3, Tilburg University, School of Economics and Management.
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    Keywords

    Correlation Matrix; Kronecker Product; MTMM; Portfolio Choice;

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