Are all (non-explosive) time series either stationary around a deterministic trend or random walks?
If I run the ADF test and I can't reject the null of non-stationarity does it imply the series is a random walk?
In particular, if I run the ADF after detrending a series but it still gives me non-stationarity, does it imply that the series is a random walk or may I just have misspecified the trend? (the problem is that it is always possible to find a trend complicated enough that the series always looks stationary).
I know these are a lot of questions but they are all related (by my poor understanding of time series). No need to answer all of them.