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Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case

Listed author(s):
  • Hafner, C. M.
  • Linton, O.

We propose a Kronecker product structure for large covariance or correlation matrices. One feature of this model is that it scales logarithmically with dimension in the sense that the number of free parameters increases logarithmically with the dimension of the matrix. We propose an estimation method of the parameters based on a log-linear property of the structure, and also a quasi-maximum likelihood estimation (QMLE) method. We establish the rate of convergence of the estimated parameters when the size of the matrix diverges. We also establish a central limit theorem (CLT) for our method. We derive the asymptotic distributions of the estimators of the parameters of the spectral distribution of the Kronecker product correlation matrix, of the extreme logarithmic eigenvalues of this matrix, and of the variance of the minimum variance portfolio formed using this matrix. We also develop tools of inference including a test for over-identification. We apply our methods to portfolio choice for S&P500 daily returns and compare with sample covariance-based methods and with the recent Fan, Liao, and Mincheva (2013) method.

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File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1664.pdf
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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 1664.

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Date of creation: 09 Nov 2016
Handle: RePEc:cam:camdae:1664
Note: obl20
Contact details of provider: Web page: http://www.econ.cam.ac.uk/

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  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. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
  3. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
  4. Amemiya, Takeshi, 1983. "Partially generalized least squares and two-stage least squares estimators," Journal of Econometrics, Elsevier, vol. 23(2), pages 275-283, October.
  5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  6. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
  7. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
  8. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-974.
  9. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
  10. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
  11. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
  12. 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.
  13. Chenlei Leng & Cheng Yong Tang, 2012. "Sparse Matrix Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1187-1200, September.
  14. Gerard, David & Hoff, Peter, 2015. "Equivariant minimax dominators of the MLE in the array normal model," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 32-49.
  15. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
  16. Anders Bredahl Kock & Haihan Tang, 2014. "Inference in High-dimensional Dynamic Panel Data Models," CREATES Research Papers 2014-58, Department of Economics and Business Economics, Aarhus University.
  17. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.
  18. Yin, Jianxin & Li, Hongzhe, 2012. "Model selection and estimation in the matrix normal graphical model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 119-140.
  19. M. Browne & A. Shapiro, 1991. "Invariance of covariance structures under groups of transformations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 345-355, December.
  20. 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.
  21. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  22. Yang Ning & Han Liu, 2013. "High-dimensional semiparametric bigraphical models," Biometrika, Biometrika Trust, vol. 100(3), pages 655-670.
  23. Linton, Oliver & McCrorie, J. Roderick, 1995. "Differentiation of an Exponential Matrix Function," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1182-1185, October.
  24. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
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