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Weak diffusion limits of dynamic conditional correlation models

Author

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  • Christian M. Hafner

    (Université catholique de Louvain, ISBA & CORE)

  • Sebastien Laurent

    (Aix-Marseille University (Aix-Marseille School of Economics))

  • Francesco Violante

    (Aarhus University and CREATES)

Abstract

The properties of dynamic conditional correlation (DCC) models are still not entirely understood. 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 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.

Suggested Citation

  • Christian M. Hafner & Sebastien Laurent & Francesco Violante, 2015. "Weak diffusion limits of dynamic conditional correlation models," CREATES Research Papers 2015-03, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-03
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    References listed on IDEAS

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    Cited by:

    1. 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.
    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. 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.
    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.

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    More about this item

    Keywords

    cDCC; Weak diffusion limits; QAML; CCC; GARCH diffusion;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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