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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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    Keywords

    score; correlation; matrix logarithm; identification;
    All these keywords.

    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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