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Estimation of a multiplicative correlation structure in the large dimensional case

Author

Listed:
  • Hafner, Christian

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Linton, Oliver

    (University of Cambridge)

  • Tang, Haihan

    (Fudan University)

Abstract

We propose a Kronecker product model for correlation or covariance matrices in the large dimensional 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 rates of convergence and central limit theorems (CLT) for our estimators in the large dimensional case. A specification test and tools for Kronecker product model selection and inference are provided. In a 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, Christian & Linton, Oliver & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," LIDAM Reprints ISBA 2020028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020028
    DOI: https://doi.org/10.1016/j.jeconom.2019.12.012
    Note: In: Journal of Econometrics - Vol. 217, no.2, p. 431-470 (2020)
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    Cited by:

    1. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    2. Hafner, Christian M. & Wang, Linqi, 2023. "A dynamic conditional score model for the log correlation matrix," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Cai, Zhanrui & Li, Changcheng & Wen, Jiawei & Yang, Songshan, 2024. "Asset splitting algorithm for ultrahigh dimensional portfolio selection and its theoretical property," Journal of Econometrics, Elsevier, vol. 239(2).
    4. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    5. Yang, Guang & Feng, Long, 2025. "Region detection and image clustering via sparse Kronecker product decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 211(C).
    6. 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.

    More about this item

    Keywords

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    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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