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Weak Diffusion Limits of Dynamic Conditional Correlation Models

Author

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  • Hafner, Christian
  • Laurent, Sebastien
  • Violante, Francesco

Abstract

The properties of dynamic conditional correlation (DCC) models, introduced more than a decade ago, are still not entirely known. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a non-degenerate diffusion limit can be obtained. Alternative sets of conditions are considered for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the often used quasi approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may provide reasonable approximations for sufficiently large frequencies and sample sizes.
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Suggested Citation

  • Hafner, Christian & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits of Dynamic Conditional Correlation Models," LIDAM Reprints ISBA 2017014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2017014
    Note: In : Econometric Theory, vol. 33, p. 691-716 (2017)
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    Cited by:

    1. Tao Chen & Yixuan Li & Renfang Tian, 2023. "A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics," Mathematics, MDPI, vol. 11(20), pages 1-27, October.
    2. Haoyuan Wang & Chen Liu & Minh-Ngoc Tran & Chao Wang, 2025. "Deep Learning Enhanced Multivariate GARCH," Papers 2506.02796, arXiv.org.
    3. Yinhao Wu & Ping He, 2024. "The continuous-time limit of quasi score-driven volatility models," Papers 2409.14734, arXiv.org, revised Jun 2025.
    4. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    5. Ding, Y., 2020. "Diffusion Limits of Real-Time GARCH," Cambridge Working Papers in Economics 20112, Faculty of Economics, University of Cambridge.
    6. Ding, Yashuang (Dexter), 2023. "A simple joint model for returns, volatility and volatility of volatility," Journal of Econometrics, Elsevier, vol. 232(2), pages 521-543.
    7. Hafner, Christian M. & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(3), pages 691-716, June.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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