# differencing in sARIMA models

Im currently trying to fit unemployment data to a sARIMA model. Unemployment has usual yearly seasonal trends so a seasonal difference is given. Log transformation is applied to minimize the errors

The data is still non-stationary so a first difference is applied. After inspecting the ACF/PACF im unsure how to proceed.

to the naked (novice) eye the ACF looks non-stationary, using a kpss however gives the following results:

#######################
# KPSS Unit Root Test #
#######################

Test is of type: mu with 5 lags.

Value of test-statistic is: 0.0503

Critical value for a significance level of:
10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739


edit: an adf test shows however that the data IS stationary.

and the kpss test confirms my results that the data is non-stationary.

Is it possible to apply a 2nd first order difference on already seasonally + first differenced data? Some litterature says nothing about it, while others say not to (but give no reason).

If it is not allowed; why? How does one continue from this point to get stationary data?