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Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model

Author

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  • Peter Reinhard Hansen

    (University of North Carolina at Chapel Hill, United States)

  • Pawel Janus

    (UBS Global Asset Management, Zürich, Switzerland)

  • Siem Jan Koopman

    (VU University Amsterdam, the Netherlands)

Abstract

We propose a novel multivariate GARCH model that incorporates realized measures for the variance matrix of returns. The key novelty is the joint formulation of a multivariate dynamic model for outer-products of returns, realized variances and realized covariances. The updating of the variance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while each innovation still impacts all elements of the variance matrix. Monte Carlo evidence for parameter estimation based on different small sample sizes is provided. We illustrate the model with an empirical application to a portfolio of 15 U.S. financial assets.

Suggested Citation

  • Peter Reinhard Hansen & Pawel Janus & Siem Jan Koopman, 2016. "Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model," Tinbergen Institute Discussion Papers 16-061/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20160061
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    13. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    14. repec:hal:journl:peer-00732537 is not listed on IDEAS
    15. Siem Jan Koopman & Marcel Scharth, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 76-115, December.
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    19. Borus Jungbacker & Siem Jan Koopman, 2006. "Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 385-408.
    20. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, September.
    21. 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.
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    Cited by:

    1. Bauwens, Luc & Xu, Yongdeng, 2023. "DCC- and DECO-HEAVY: Multivariate GARCH models based on realized variances and correlations," International Journal of Forecasting, Elsevier, vol. 39(2), pages 938-955.
    2. Umlandt, Dennis, 2023. "Score-driven asset pricing: Predicting time-varying risk premia based on cross-sectional model performance," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    4. Manabu Asai & Michael McAleer, 2022. "Bayesian Analysis of Realized Matrix-Exponential GARCH Models," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 103-123, January.
    5. Asai Manabu & So Mike K. P., 2023. "Realized BEKK-CAW Models," Journal of Time Series Econometrics, De Gruyter, vol. 15(1), pages 49-77, January.
    6. Marius Matei & Xari Rovira & Núria Agell, 2019. "Bivariate Volatility Modeling with High-Frequency Data," Econometrics, MDPI, vol. 7(3), pages 1-15, September.
    7. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    8. Emilija Dzuverovic & Matteo Barigozzi, 2023. "Hierarchical DCC-HEAVY Model for High-Dimensional Covariance Matrices," Papers 2305.08488, arXiv.org, revised Jul 2024.
    9. Vogler, Jan & Golosnoy, Vasyl, 2023. "Unrestricted maximum likelihood estimation of multivariate realized volatility models," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1063-1074.
    10. Alexander Georges Gretener & Matthias Neuenkirch & Dennis Umlandt, 2022. "Dynamic Mixture Vector Autoregressions with Score-Driven Weights," Working Paper Series 2022-02, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    11. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    12. Gorgi, P. & Koopman, S.J., 2023. "Beta observation-driven models with exogenous regressors: A joint analysis of realized correlation and leverage effects," Journal of Econometrics, Elsevier, vol. 237(2).
    13. BAUWENS Luc, & XU Yongdeng,, 2019. "DCC-HEAVY: A multivariate GARCH model based on realized variances and correlations," LIDAM Discussion Papers CORE 2019025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org, revised Feb 2025.
    15. 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.
    16. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    17. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    18. Dennis Umlandt, 2020. "Likelihood-based Dynamic Asset Pricing: Learning Time-varying Risk Premia from Cross-Sectional Models," Working Paper Series 2020-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    19. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2021. "Exploring volatility of crude oil intra-day return curves: a functional GARCH-X Model," MPRA Paper 109231, University Library of Munich, Germany.
    20. Hartkopf, Jan Patrick & Reh, Laura, 2023. "Challenging golden standards in EWMA smoothing parameter calibration based on realized covariance measures," Finance Research Letters, Elsevier, vol. 56(C).

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    More about this item

    Keywords

    high-frequency data; multivariate GARCH; multivariate volatility; realised covariance; score; Wishart density;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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