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Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case

Author

Listed:
  • Hafner, C.
  • Linton, O.
  • Tang, H.
Abstract
We propose a Kronecker product model for correlation or covariance matrices in the large dimension case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD) estimator based on a log-linear property of the model, as well as a one-step estimator, which is a one-step approximation to the quasi-maximum likelihood estimator (QMLE).We establish the rate of convergence and a central limit theorem (CLT) for our estimators in the large dimensional case. A specification test and tools for Kronecker product model selection and inference are provided. In an Monte Carlo study where a Kronecker product model is correctly specified, our estimators exhibit superior performance. In an empirical application to portfolio choice for S&P500 daily returns, we demonstrate that certain Kronecker product models are good approximations to the general covariance matrix.

Suggested Citation

  • Hafner, C. & Linton, O. & Tang, H., 2018. "Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1878, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1878
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    References listed on IDEAS

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    Cited by:

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    3. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    4. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.

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    More about this item

    Keywords

    Correlation matrix; Kronecker product; Matrix logarithm; Multiway; array data; Portfolio choice; Sparsity;
    All these keywords.

    JEL classification:

    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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