I am trying to analyse a time series. I want to get only quantitative results (so, I'm excluding things like "looking at this plot we can note..." or "as you can see in the chart ...").
In my job, I analyse stationarity and persistence. First, I run ADF test and get "stationary" or "non-stationary" as results. Then, I need to work on persistence. To do so, I use ACF.
My question is: suppose I got "non-stationary" time series. Is it right to run ACF on it (without differencing)? I would like to comment upon stationarity and persistency without having to differentiate (so, just run tests on the original data and getting "answers" like "strong positive persistence", "weak negative persistence", ...).
I am writing here my question since I am working on close prices, returns and volatility. The time series are about them and I am trying to see if there are "better" time series than others (looking at general time series characteristics as non-stationarity...).
Thanks to who will even just read my question.