<p>Nonstationarity and outlying observations are commonly encountered in financial time series. It is thus expected that models are able to accommodate these stylized facts and the techniques used are suitable to specify such models. In this paper we relax the assumption of stationarity and consider the problem of detecting smooth changes in the unconditional variance in the presence of outliers. It is found by simulation that the misspecification test for constancy of the unconditional variance in GARCH models can be severely adversely affected in the presence of additive outliers. An outlier robust specification procedure is also proposed to mitigate the effects of outliers for building multiplicative time-varying volatility models. The outlier robust variant of the test is shown to perform better than the conventional test in terms of size and power. An application to commodity returns illustrates the usefulness of the robust specification procedure.</p>