  We propose a new asymptotic test to assess the stationarity of a time series'
mean that is applicable in the presence of both heteroscedasticity and
short-range dependence. Our test statistic is composed of Gini's mean
difference of local sample means. To analyse its asymptotic behaviour, we
develop new limit theory for U-statistics of strongly mixing triangular arrays
under non-stationarity. Most importantly, we show asymptotic normality of the
test statistic under the hypothesis of a constant mean and prove the test's
consistency against a very general class of alternatives, including both smooth
and abrupt changes in the mean. We propose estimators for all parameters
involved, including an adapted subsampling estimator for the long run variance,
and show their consistency. Our procedure is practically evaluated in an
extensive simulation study and in two data examples.
