Very interesting article! I have two doubts on time series stationarity and I would be grateful I you helped me:
1) I didn't understand the exact difference between cyclic and seasonal time series. I can understand a seasonal time series, that is a time series which repeats after a given period of time, but I don't understand cyclic time series.
2) Regarding the statistical tests in general, including the Adfuller test, I have read somewhere that the p-value specifies if the test is valid. Then, the acceptance or the rejection of the null hypothesis is done on the test statistic. I mean, if p-value < 0.05 and test_statistic < critical_value then the time series is stationary. If p-value > 0.05 the test does not have sense. Is this true?