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Journal Articles Econometric Theory Year : 2017

Weak Diffusion Limits of Dynamic Conditional Correlation Models

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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Dates and versions

hal-01590010 , version 1 (19-09-2017)

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Christian M. Hafner, Sébastien Laurent, Francesco Violante. Weak Diffusion Limits of Dynamic Conditional Correlation Models. Econometric Theory, 2017, 33 (03), pp.691--716. ⟨10.1017/S0266466616000128⟩. ⟨hal-01590010⟩
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