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QML INFERENCE FOR VOLATILITY MODELS WITH COVARIATES

Published online by Cambridge University Press:  01 February 2018

Christian Francq  and
Le Quyen Thieu
Christian Francq*
Affiliation:
CREST and Université de Lille, RiskDesign and Université Pierre et Marie Curie
Le Quyen Thieu
Affiliation:
CREST and Université de Lille, RiskDesign and Université Pierre et Marie Curie
*
*Address correspondence to Christian Francq, 5 Avenue Henry Le Chatelier 91120 Plaiseau, France; e-mail: [email protected].
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Abstract

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.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 1 , February 2019 , pp. 37 - 72
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

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).

References

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