# Effect of differencing on prediction intervals in ARIMA models

I am sitting with a couple of time-series that I am analysing using ARIMA models. I have a question regarding prediction intervals. When predicting using a model that takes a first difference (a SARIMA(1,1,0)x(1,0,0) model), I get an increasing size of the prediction interval. Without I get a very constant and narrow band (see below):

The corresponding results are as follows:

Can anyone explain why the band is so constant? First I thought it was because of a large significant MA coefficient. This, however, I removed and the "problem" persisted. Then I though it was because the ARIMA without differencing automatically included an intercept. However, again, when I specified include.mean = FALSE, nothing changed.

Any help would be appreciated.

• When forecasting, you deal with prediction intervals rather than confidence intervals. The two are not the same. – Richard Hardy Aug 17 '16 at 13:46
• Hey Richard. Thanks for pointing out my imprecision. I have now edited the post accordingly – pkpkPPkafa Aug 18 '16 at 7:02