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Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates

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  • Heejoon Han

    ()
    (National University of Singapore)

  • Dennis Kristensen

    ()
    (University College London and CREATES)

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 regression coefficients entering the volatility equation are consistent and normally distributed in large samples independently of the degree of persistence. This implies that standard inferential tools, such as t-statistics, do not have to be adjusted to the level of persistence. On the other hand, the intercept in the volatility equation is not identifi?ed when the covariate is non-stationary which is akin to the results of Jensen and Rahbek (2004, Econometric Theory 20) who develop similar results for the pure GARCH model with explosive volatility.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-25.

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Length: 28 Heejoon Han and Dennis Kristensen
Date of creation: 18 May 2012
Date of revision:
Handle: RePEc:aah:create:2012-25

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: GARCH; Persistent covariate; Fractional integration; Quasi-maximum likelihood estimator; Asymptotic distribution theory.;

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