We introduce a smoothed version of the quasi maximum likelihood estimator (QMLE) in order to fit heteroschedastic time series with possibly vanishing conditional variance. We apply this procedure to a finite-order autoregressive process with linear ARCH errors. We prove both the almost sure consiistency and the asymptotic normality of our estimator. This estimator is more robust that QMLE with the same type of assumptions. A numerical study confirms the qualities of our procedure.