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Weak diffusion limits of dynamic conditional correlation models

Author

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  • Christian M. HAFNER
  • Sébastien LAURENT
  • Francesco VIOLANTE

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 nondegenerate 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

  • Christian M. HAFNER & Sébastien LAURENT & Francesco VIOLANTE, 2017. "Weak diffusion limits of dynamic conditional correlation models," LIDAM Reprints CORE 2866, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2866
    Note: In : Econometric Theory, 33, 691-716, 2017
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    References listed on IDEAS

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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. 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.
    3. Yinhao Wu & Ping He, 2024. "The continuous-time limit of quasi score-driven volatility models," Papers 2409.14734, arXiv.org.
    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.

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    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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