Suppose I have a time series: $$ z_t = 0.01 t + 0.9 z_{t-1} + e_t $$ where $e_t$ is $N(0,1)$.
Now, this series is non-stationary as can be easily be checked with an ADF test (using statsmodels
for example). My question is, if ADF tells me the that series is non-stationary, can I find the reason it is non-stationary? Is there a way I can find out if the series is $I(1)$ or $I(2)$ or has a drift with trend if it is not easily visible from a plot of the time series (unlike the example here) or do I need to run ADF tests on differences and so on?