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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.

Jarom
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  • 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". – ColorStatistics Dec 05 '18 at 17:02
  • @ColorStatistics the first-differenced series is covariance stationary. It doesn't have a trend. – Jarom Dec 05 '18 at 19:23
  • Which test did you use? If ADF, what is the conclusion for the test with and without trend? – ColorStatistics Dec 05 '18 at 20:06
  • @ColorStatistics Yes, I used ADF. Before differencing p-value = 0.168 after differencing p-value =0.00. – Jarom Dec 05 '18 at 20:09
  • 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 https://stats.stackexchange.com/questions/131148/the-difference-between-the-three-augmented-dickey-fuller-test-none-drift-trend – ColorStatistics Dec 05 '18 at 20:19
  • I should have said ... there are the following variations of the ADF test: 1) no constant, no trend, 2) constant, no trend and 3) constant, trend... See if you can figure out which ADF you ran and revisit your initial puzzle with that added insight. Also keep in mind that the ADF is sensitive to the number of lags you include in the test. You should think about how many lags you should include in the ADF test to deal with serial correlation in order to conduct a valid test. Performing the ADF test correctly is half the battle in your case as it should shed light on your questions. – ColorStatistics Dec 05 '18 at 20:49

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