I want to estimate an ARIMA model. The dependent variable itself already is a log first difference. However, after testing KPSS and Augmented Dickey Fuller, it is not stationary, only for 0 lags. (also, the plot does not look stationary at all). Is it statistically plausible to take the first differences again? After using first differences, the tests show stationarity even after 10 lags, and the plots look much like stationarity. Or is it usually enough that the stationarity-tests show stationarity for 0 lags?
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