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Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates

Authors: Heejoon Han and Dennis Kristensen
Date: 17 May 2013
Type: cemmap Working Paper, CWP18/13
DOI: 10.1920/wp.cem.2013.1813

Abstract

This paper 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 dx; in particular, we allow for both stationary and non-stationary 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.

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Now published:
Heejoon Han and Dennis Kristensen July 2014, Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates, Journal Article, Taylor & Francis Online

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