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The Conditional Autoregressive F-Riesz Model for Realized Covariance Matrices

Author

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  • Anne Opschoor
  • André Lucas
  • Luca Rossini

Abstract

We introduce a new model for the dynamics of fat-tailed (realized) covariance-matrix-valued time-series using the F-Riesz distribution. The model allows for heterogeneous 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. 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 turn out to be empirically relevant: they produce significant in-sample and out-of-sample likelihood increases, ex-post portfolio standard deviations that are in the global minimum variance model confidence set, and economic differences that are either in favor of the new model or competitive with a range of benchmark models.

Suggested Citation

  • Anne Opschoor & André Lucas & Luca Rossini, 2025. "The Conditional Autoregressive F-Riesz Model for Realized Covariance Matrices," Journal of Financial Econometrics, Oxford University Press, vol. 23(2), pages 177-190.
  • Handle: RePEc:oup:jfinec:v:23:y:2025:i:2:p:177-190.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbae023
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    More about this item

    Keywords

    covariance matrix distributions; tail heterogeneity; (Inverse) Riesz distribution; 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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