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Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution

Author

Listed:
  • Andre Lucas

    (Vrije Universiteit Amsterdam)

  • Anne Opschoor

    (Vrije Universiteit Amsterdam)

  • Luca Rossini

    (University of Milan)

Abstract
We introduce a novel model for the dynamics of fat-tailed (realized) covariance-matrix-valued time series using the new F-Riesz distribution. The model allows for different tail behavior across the coordinates of the covariance matrix via two vector-valued degrees of freedom parameters, thus generalizing the familiar Wishart and matrix-F distributions by introducing heterogeneous tail behavior. We show that the filter implied by the new model is invertible and that a two-step targeted maximum likelihood estimator is consistent. Applying the new F-Riesz model to U.S. stocks, both tail-heterogeneity and tail-fatness are empirically relevant and produce large in-sample and out-of-sample likelihood increases and lower ex-post portfolio standard deviations compared to static models or models with homogeneous tail behavior

Suggested Citation

  • Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    • Handle: RePEc:tin:wpaper:20210010
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    References listed on IDEAS

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    Cited by:

    1. Abdelhamid Hassairi & Fatma Ktari & Raoudha Zine, 2022. "On the Gaussian representation of the Riesz probability distribution on symmetric matrices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 609-632, December.
    2. Anne Opschoor & Dewi Peerlings & Luca Rossini & Andre Lucas, 2024. "Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution," Tinbergen Institute Discussion Papers 24-049/III, Tinbergen Institute.

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    More about this item

    Keywords

    matrix distributions; tail heterogeneity; (inverse) Riesz; fat-tails; realized covariance matrices;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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