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WEAK DIFFUSION LIMITS OF DYNAMIC CONDITIONAL CORRELATION MODELS

Published online by Cambridge University Press:  13 June 2016

Christian M. Hafner*
Affiliation:
Université catholique de Louvain
Sebastien Laurent
Affiliation:
Aix-Marseille University
Francesco Violante
Affiliation:
Aarhus University
*
*Address correspondance to Christian M. Hafner, Université catholique de Louvain, ISBA and CORE, B-1348 Louvain-la-Neuve, Belgium, e-mail: Christian.hafner@uclouvain.be.
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Abstract

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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.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program Investissements d’Avenir supervised by the Agence Nationale de la Recherche.

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