Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates

Heejoon Han and Dennis Kristensen

Journal of Business & Economic Statistics, 2014, vol. 32, issue 3, 416-429

Abstract: This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE's) of the GARCH model augmented by including an additional explanatory variable-the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as captured by its long-memory parameter d x ; in particular, we allow for both stationary and nonstationary covariates. We show that the QMLE's of the parameters entering the volatility equation are consistent and mixed-normally distributed in large samples. The convergence rates and limiting distributions of the QMLE's depend on whether the regressor is stationary or not. However, standard inferential tools for the parameters are robust to the level of persistence of the regressor with t -statistics following standard Normal distributions in large sample irrespective of whether the regressor is stationary or not. Supplementary materials for this article are available online.

Date: 2014
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Related works:
Working Paper: Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates (2013)
Working Paper: Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates (2013)
Working Paper: Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:32:y:2014:i:3:p:416-429

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DOI: 10.1080/07350015.2014.897954

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