Can One Really Estimate Nonstationary GARCH Models ?
Jensen and Rahbek (2004a) claim that consistency and asymptotic normality hold for the quasi-maximumlikelihood estimator (QMLE) of (!0, 0) in nonstationary ARCH(1) models. In fact their result onlyconcerns a constrained QMLE, in which the intercept is fixed, and under a reinforced nonstationaritycondition. Under this condition, we prove that the standard QMLE of 0 is strongly consistent andasymptotically normal. Numerical experiments reveal that QMLE of !0 is likely to be inconsistent.
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