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I have a dataset of stock prices and wanted to make it stationary.

I did a difference using lag 1 and then did the difference again using lag 1.

After the first differencing the Augmented Dickey Fuller test for unit root had a p-value of 0.0001, yet the ACF had a sinusoid - I feel like this is telling me that my differences (my volatilty) have a periodicity, my variance is non-stationary - is this a correct deduction? How come the sinusoid appears but the DF test still has a low p-value?

The ACF for the raw data was a negative gradient straight line. So did the 1st order difference create or did it expose seasonality/periodicity in the data (seasonality in the variance)?

EDIT : I have just read that cyclic behaviour does not equal seasonality. So potentially even with the cycles in the ACF - the 1st order difference can still be classed as stationary?

Finally: Can I look at the absolute value of the differences to avoid negative values, when I come to build my GARCH model? Can I remove the MA from my dataset to make it stationary?

Answers to my questions appreciated!

Raw Data - No Differencing Raw Data - No Differencing After 1st differencing After 1st differencing After 2nd differencing After 2nd differencing

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