Whether or not a time series is weakly stationary has long been a question of major interest in the field of time series analysis. Stationary time series can be sufficiently described by means of autoregressive moving average (ARMA) processes. When modelling temporal correlations of GNSS observation noise, the applicability of ARMA processes depends on the stationarity of residual time series from GNSS data analysis. According to the property that stationary processes have homogenous variances, statistical inferences on stationarity can be made by testing for homogeneity of variance (HOV). In addition, considering a time series as a realisation of a stochastic process, stationarity can be assessed by testing for stochastic trends using unit root tests. Based on representative data simulations, this paper analyses the empirical size and power of commonly used HOV and unit root tests. The results show that the performance of the HOV test is strongly affected by serial correlations, whereas the unit root test produces high power without significant size distortions.