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

  • Heejoon Han
  • Dennis Kristensen

    (Institute for Fiscal Studies and University College London)

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 entereing 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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File URL: http://www.cemmap.ac.uk/wps/cwp181313.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP18/13.

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Date of creation: May 2013
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Handle: RePEc:ifs:cemmap:18/13
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