Can a timeseries with a clear trend be considered stationary? I performed a augmented Dickey-Fuller test on a timeseries (that clearly has a trend) and, from the results, it suggests it is stationary (p-value = 0.01). Is this possible?
    Augmented Dickey-Fuller Test

data:  timeseries_1
Dickey-Fuller = -5.7857, Lag order = 14, p-value = 0.01
alternative hypothesis: stationary



From the help page:

The general regression equation which incorporates a constant and
a linear trend is used and the t-statistic for a first order
autoregressive coefficient equals one is computed.

That is, adf.test() fits a regression using an intercept, a trend (!) and the first $k$ autoregressive terms in the series. Only in this context does it test whether the first autoregressive parameter is equal to one, which would indicate nonstationarity.
Thus, a trended series can definitely be stationary in the sense of tseries::adf.test(), namely if it is stationary after accounting for the trend.
