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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):

Graphs

The corresponding results are as follows:

Results

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.

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  • $\begingroup$ When forecasting, you deal with prediction intervals rather than confidence intervals. The two are not the same. $\endgroup$ – Richard Hardy Aug 17 '16 at 13:46
  • $\begingroup$ Hey Richard. Thanks for pointing out my imprecision. I have now edited the post accordingly $\endgroup$ – pkpkPPkafa Aug 18 '16 at 7:02
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In general, forecast intervals from ARIMA models will increase as the forecast horizon increases. For stationary models (i.e., with no differencing), they will converge so forecast intervals for long horizons are all essentially the same. If there is some differencing, you are assuming the series is non-stationary, and the forecast intervals will continue to diverge into the future.

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  • $\begingroup$ Hey Rob. Thanks so much for the response. I appreciate the explanation. $\endgroup$ – pkpkPPkafa Aug 18 '16 at 7:03
  • $\begingroup$ Dear Rob, I have related but little bit advanced issue, maybe you would have some comments on that ? stats.stackexchange.com/questions/261102/… $\endgroup$ – Brano Cuchran Feb 22 '17 at 10:15

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