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I've developed a reasonable time-series model on first differenced data. The end goal is to be able to forecast an actual value, not a differenced value.

From reading other posts I learned that the first step is to add the prediction of the model to the previous month's value.

The problem that I run into, and haven't been able to find an answer to, is that the trend that I differenced to get rid of has no representation in my predicted values. This causes my prediction to be consistently too high (my data has a negative trend).

I've looked into decomposition to get a trend, but I'm not sure how/if the trend component would be helpful in making my model more accurate.

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  • $\begingroup$ Is your first-differenced series covariance stationary? If it is, there should be no trend in it. If it isn't, then your regression in first-differences is a "spurious regression". $\endgroup$ – ColorStatistics Dec 5 '18 at 17:02
  • $\begingroup$ @ColorStatistics the first-differenced series is covariance stationary. It doesn't have a trend. $\endgroup$ – Jarom Dec 5 '18 at 19:23
  • $\begingroup$ Which test did you use? If ADF, what is the conclusion for the test with and without trend? $\endgroup$ – ColorStatistics Dec 5 '18 at 20:06
  • $\begingroup$ @ColorStatistics Yes, I used ADF. Before differencing p-value = 0.168 after differencing p-value =0.00. $\endgroup$ – Jarom Dec 5 '18 at 20:09
  • $\begingroup$ These are several variants of the ADF test, and they tell you different things. There is one with trend; another one without trend. See this post stats.stackexchange.com/questions/131148/… $\endgroup$ – ColorStatistics Dec 5 '18 at 20:19

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