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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.

enter image description here

enter image description here

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?

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One doesn't assume a transformation to minimize the errors. One examines the errors from a tentative model and thus it may be necessary to simply transform the data via Box-Cox as I answered here http://stats.stackexchange.com/questions/18844/when-and-why-to-take-the-log-of-a-distribution-of-numbers.

Often times simple Intervention Detection remedies the apparent need for a Box-Cox transformation as was presented here http://autobox.com/cms/index.php/blog/entry/u-didnt-need-logs .

Differencing is a form of a transformation that often is unwarranted while a simple de-meaning might be more applicable. See Evaluating if time series need differencing

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  • $\begingroup$ Thank you for your answer. I have actually already tried doing a Box-Cox transformation on the data and applying no differencing, then running a auto.arima (to check different models) on the transformed data. However the residuals of all the models are correlated and not normally distributed. Do you have any recommendations on what my next step could be (if first differencing 3 or more times is out of the question)? Would that be outlier detection and intervention as you mentioned? The data I have seems particularly hard to work with. $\endgroup$ – kroneckersdelta Apr 10 at 15:30
  • $\begingroup$ if u post you data in a csv format i will try and help further. The auto.arima program assumes many many things including the absence of pulses, level shifts, seasonal pulses and local time trends and thusly so may be of little use. As they say "Mileage may vary ! " $\endgroup$ – IrishStat Apr 10 at 18:14

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