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  • Christian Francq (a1) and Le Quyen Thieu (a1)


The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive tests for the significance of the parameters. In particular, the relevance of the exogenous variables can be assessed. The results are obtained without assuming that the innovations are independent, which allows conditioning on different information sets. Monte Carlo experiments and applications to financial series illustrate the asymptotic results. In particular, an empirical study demonstrates that the realized volatility can be a helpful covariate for predicting squared returns.


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*Address correspondence to Christian Francq, 5 Avenue Henry Le Chatelier 91120 Plaiseau, France; e-mail:


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We are grateful to the Editor, Associate Editor and anonymous reviewers for useful comments and suggestions. Christian Francq gratefully acknowledges the financial support from the labex ECODEC and the Agence Nationale de la Recherche (ANR) via the Project MultiRisk (ANR-16-CE26-0015-02).



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  • Christian Francq (a1) and Le Quyen Thieu (a1)


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