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A multivariate realized GARCH model

Author

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  • Archakov, Ilya
  • Hansen, Peter Reinhard
  • Lunde, Asger

Abstract

We propose a novel class of multivariate GARCH models that incorporate realized measures of volatility and correlations. The key innovation is an unconstrained vector parametrization of the conditional correlation matrix, which enables the use of factor models for correlations. This approach elegantly addresses the main challenge faced by multivariate GARCH models in high-dimensional settings. As an illustration, we explore block correlation matrices that naturally simplify to linear factor models for the conditional correlations. The model is applied to the returns of nine assets, and its in-sample and out-of-sample performance compares favorably against several popular benchmarks.

Suggested Citation

  • Archakov, Ilya & Hansen, Peter Reinhard & Lunde, Asger, 2026. "A multivariate realized GARCH model," Journal of Econometrics, Elsevier, vol. 254(PA).
    • Handle: RePEc:eee:econom:v:254:y:2026:i:pa:s0304407625000946
    DOI: 10.1016/j.jeconom.2025.106040
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    1. is not listed on IDEAS
    2. Hafner, Christian M. & Wang, Linqi, 2023. "A dynamic conditional score model for the log correlation matrix," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Tong, Chen & Hansen, Peter Reinhard, 2023. "Characterizing correlation matrices that admit a clustered factor representation," Economics Letters, Elsevier, vol. 233(C).
    4. Didit B. Nugroho & Bambang Susanto & Faldy Tita & Takayuki Morimoto, 2026. "Real-time return extensions of realized GARCH models for improved risk management in asset markets," Journal of Asset Management, Palgrave Macmillan, vol. 27(2), pages 1-19, June.
    5. Jiawen Luo & Shengjie Fu & Oguzhan Cepni & Rangan Gupta, 2025. "The Role of Uncertainty in Forecasting Realized Covariance of US State-Level Stock Returns: A Reverse-MIDAS Approach," Working Papers 202501, University of Pretoria, Department of Economics.
    6. Han Chen & Yijie Fei & Jun Yu, 2026. "Multivariate Stochastic Volatility Model with Block Correlations," Working Papers 202638, University of Macau, Faculty of Business Administration.
    7. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    8. Ilya Archakov, 2026. "A Robust Similarity Estimator," Papers 2601.12198, arXiv.org.
    9. Emilija Dzuverovic & Matteo Barigozzi, 2023. "Hierarchical DCC-HEAVY Model for High-Dimensional Covariance Matrices," Papers 2305.08488, arXiv.org, revised Jul 2024.
    10. Laura Capera Romero & Anne Opschoor, 2025. "Revisiting EWMA in High-Frequency Portfolio Optimization: A Comparative Assessment," Tinbergen Institute Discussion Papers 25-041/III, Tinbergen Institute.
    11. De Nard, Gianluca & Engle, Robert F. & Ledoit, Olivier & Wolf, Michael, 2022. "Large dynamic covariance matrices: Enhancements based on intraday data," Journal of Banking & Finance, Elsevier, vol. 138(C).
    12. Chen Tong & Peter Reinhard Hansen, 2025. "Dynamic Factor Correlation Model," Papers 2503.01080, arXiv.org.

    More about this item

    Keywords

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • 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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