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

Author

Listed:
  • 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.

Suggested Citation

  • Heejoon Han & Dennis Kristensen, 2012. "Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates," CREATES Research Papers 2012-25, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2012-25
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    More about this item

    Keywords

    GARCH; Persistent covariate; Fractional integration; Quasi-maximum likelihood estimator; Asymptotic distribution theory.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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