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New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

Author

Listed:
  • Pawel Janus

    (UBS Global Asset Management, the Netherlands)

  • André Lucas

    (VU University Amsterdam)

  • Anne Opschoor

    (VU University Amsterdam, the Netherlands)

  • Dick J.C. van Dijk

    (Erasmus University Rotterdam, the Netherlands)

Abstract

We develop a new model for the multivariate covariance matrix dynamics based on daily return observations and daily realized covariance matrix kernels based on intraday data. Both types of data may be fat-tailed. We account for this by assuming a matrix-F distribution for the realized kernels, and a multivariate Student’s t distribution for the returns. Using generalized autoregressive score dynamics for the unobserved true covariance matrix, our approach automatically corrects for the effect of outliers and incidentally large observations, both in returns and in covariances. Moreover, by an appropriate choice of scaling of the conditional score function we are able to retain a convenient matrix formulation for the dynamic updates of the covariance matrix. This makes the model highly computationally efficient. We show how the model performs in a controlled simulation setting as well as for empirical data. In our empirical application, we study daily returns and realized kernels from 15 equities over the period 2001-2012 and find that the new model statistically outperforms (recently developed) multivariate volatility models, both in-sample and out-of-sample. We also comment on the possibility to use composite likelihood methods for estimation if desired.

Suggested Citation

  • Pawel Janus & André Lucas & Anne Opschoor & Dick J.C. van Dijk, 2014. "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels," Tinbergen Institute Discussion Papers 14-073/IV, Tinbergen Institute, revised 19 Aug 2015.
  • Handle: RePEc:tin:wpaper:20140073
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    References listed on IDEAS

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    Cited by:

    1. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    2. P Gorgi & P R Hansen & P Janus & S J Koopman, 2019. "Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 17(1), pages 1-32.
    3. Lucas, André & Opschoor, Anne & Schaumburg, Julia, 2016. "Accounting for missing values in score-driven time-varying parameter models," Economics Letters, Elsevier, vol. 148(C), pages 96-98.

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    More about this item

    Keywords

    realized covariance matrices; heavy tails; (degenerate) matrix-F distribution; generalized autoregressive score (GAS) dynamics;
    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

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