I was trying to fit an ARMA model for some data. It was easy to spot that data is non-stationary, so I decided to conduct ADF test on it and it turns out that I was right. Then I took the first differences of the data and conduct the ADF test on new set of data, and according to the test, the data was still non-stationary. I have also checked the second differences of the data and they were stationary. That brings me to my question, is my reasoning correct? I have read somewhere that is not correct. Can somebody share their knowledge about this topic?
ADF test results confusion provides clarity as to what is being tested with the ADF test . With all statistical tests one has to know precisely what the null hypothesis is and what the alternative hypothesis is.
The cause/remedy for non-stationarity can occur in a number of ways requiring identification and remediation/treatmewnt.
There could be the need to difference , detrend , demean , filter via arma, adjust for latent deterministic structure such as pulses/level/step shifts/seasonal pulses, segment the data based upon parameter or error variance changes over time to name a few.
Take a look at this rather straightforward question How to remove non-stationarity? where the OP asked the direct question of what was needed to make his series stationary. In other words what equation/filter was sufficient to decompose the observed data to signal and noise