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A dynamic conditional score model for the log correlation matrix

Author

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  • HAFNER Christian M.,

    (Université catholique de Louvain, Belgium)

  • WANG Linqi,

    (Université catholique de Louvain, Belgium)

Abstract

This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive defi nite, even in high dimensions. For the conditional distribution of returns we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially diff erent degrees of freedom. The separation into volatility and correlation parts allows two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including nancial and alternative assets we show that the model performs well in terms of various diagnostics and speci cation tests.

Suggested Citation

  • HAFNER Christian M., & WANG Linqi,, 2019. "A dynamic conditional score model for the log correlation matrix," LIDAM Discussion Papers CORE 2019031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2019031
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2019.html
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    Cited by:

    1. is not listed on IDEAS
    2. Hansen, Peter Reinhard & Tong, Chen, 2026. "Convolution-t distributions," Journal of Econometrics, Elsevier, vol. 254(PB).
    3. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2026. "Cluster GARCH," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 44(1), pages 148-161, January.
      • Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    4. Archakov, Ilya & Hansen, Peter Reinhard & Lunde, Asger, 2026. "A multivariate realized GARCH model," Journal of Econometrics, Elsevier, vol. 254(PA).
    5. Etienne Wijler & Andre Lucas, 2025. "An Impartial Look at Asset Correlation Stability and Market Structure," Tinbergen Institute Discussion Papers 25-051/III, Tinbergen Institute.
    6. Jiawen Luo & Shengjie Fu & Oguzhan Cepni & Rangan Gupta, 2025. "The Role of Uncertainty in Forecasting Realized Covariance of US State-Level Stock Returns: A Reverse-MIDAS Approach," Working Papers 202501, University of Pretoria, Department of Economics.
    7. Chen, Han & Fei, Yijie & Yu, Jun, 2025. "Multivariate stochastic volatility models based on generalized Fisher transformation," Journal of Econometrics, Elsevier, vol. 251(C).
    8. Stollenwerk, Michael, 2026. "Probability distributions for realized covariance measures," Journal of Econometrics, Elsevier, vol. 254(PA).
    9. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.
    10. Han Chen & Yijie Fei & Jun Yu, 2026. "Multivariate Stochastic Volatility Model with Block Correlations," Working Papers 202638, University of Macau, Faculty of Business Administration.
    11. Wang, Yifu & Lu, Wanbo & Lin, Min-Bin & Ren, Rui & Härdle, Wolfgang Karl, 2024. "Cross-exchange crypto risk: A high-frequency dynamic network perspective," International Review of Financial Analysis, Elsevier, vol. 94(C).
    12. Koos B. Gubbels & Andre Lucas, 2026. "Spectral Dynamics and Regularization for High-Dimensional Copulas," Papers 2601.13281, arXiv.org.

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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • Z11 - Other Special Topics - - Cultural Economics - - - Economics of the Arts and Literature

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