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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?

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  • $\begingroup$ Very good question. One of me favorites. Reading this every night before sleep. $\endgroup$
    – John
    Jan 12 at 20:18
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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

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  • $\begingroup$ Thank you for your answer, especially for the links, they gave me a lot of information. $\endgroup$
    – ononono
    Mar 29 '20 at 20:27
  • $\begingroup$ If you like my answer then accept it to signal that when you are comfortable. $\endgroup$
    – IrishStat
    Mar 29 '20 at 21:48

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