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

Authors: Heejoon Han and Dennis Kristensen
Date: 28 July 2014
Type: Journal Article, Journal of Business & Economic Statistics, Vol. 32, No. 3, pp. 416-429
DOI: 10.1080/07350015.2014.897954

Abstract

This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLEs) 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 dx; 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.

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Previous version:
Heejoon Han and Dennis Kristensen May 2013, Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates, cemmap Working Paper, CWP18/13, Institute for Fiscal Studies

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