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

Author

Listed:
  • P Gorgi
  • P R Hansen
  • P Janus
  • S J Koopman

Abstract

We propose a novel multivariate GARCH model that incorporates realized measures for the covariance matrix of returns. The joint formulation of a multivariate dynamic model for outer-products of returns, realized variances, and realized covariances leads to a feasible approach for analysis and forecasting. The updating of the covariance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while the analysis relies on straightforward computations. In a Monte Carlo study, we show that parameters are estimated accurately for different small sample sizes. We illustrate the model with an empirical in-sample and out-of-sample analysis for a portfolio of 15 U.S. financial assets.

Suggested Citation

  • P Gorgi & P R Hansen & P Janus & S J Koopman, 2019. "Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model," Journal of Financial Econometrics, Oxford University Press, vol. 17(1), pages 1-32.
    • Handle: RePEc:oup:jfinec:v:17:y:2019:i:1:p:1-32.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nby007
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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. 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.
    3. 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).
    4. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org, revised Feb 2025.
    5. Alexander Georges Gretener & Matthias Neuenkirch & Dennis Umlandt, 2025. "Dynamic Mixture Vector Autoregressions With Score‐Driven Weights," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(4), pages 455-470, June.
    6. 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).
    7. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    8. 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.
    9. 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.
    10. Marius Matei & Xari Rovira & Núria Agell, 2019. "Bivariate Volatility Modeling with High-Frequency Data," Econometrics, MDPI, vol. 7(3), pages 1-15, September.
    11. 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.
    12. Xu, Buyun & Wu, Zhimin, 2025. "Real-time GARCH@CARR: A joint model of returns, realized measure of volatility and current intraday information," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    13. 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.
    14. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    15. Emilija Dzuverovic & Matteo Barigozzi, 2023. "Hierarchical DCC-HEAVY Model for High-Dimensional Covariance Matrices," Papers 2305.08488, arXiv.org, revised Jul 2024.
    16. 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.
    17. 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).
    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. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).
    20. 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.
    21. 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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    Keywords

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    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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