I wonder if a time series being stationary implies that there can be no upward or downward trend. It appears to me that such an implication should hold, since in order to be stationary a time series has to have a constant mean, so in general it should wiggle around the same point. Is my reasoning correct?
So for instance is it possible to get a significant result of the Dickey-Fuller test indicating that a series is stationary, but at the same time get a significant result of the Mann-Kendall trend test, which indicates that there is a trend? In what kind of situation such an outcome may arise?