# 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


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.
• That plot almost looks like it's stationary around a nonlinear trend. Does asdf.test try multiple different trend models, or is the nonlinearity gentle enough that the ADF test routine doesn't trip on it? Jul 22, 2022 at 13:26