The Arima() function in the R forecast package contains an "include.drift" parameter. Could someone explain how this is calculated and how it is included in point forecasts?

According to this post by Rob Hyndman this parameter is usally used when the series is differenced at least once. Nevertheless when I include it in forecasts for a undifferenced series it seems to produce more realistic forecasts. I would like to know why that is. Thanks in advance for any help.


The "reason" that the undifferenced model is better behaved with the "drift" parameter is that when one has an undifferenced model the drift parameter is in reality an estimate of the conditional mean AND should be properly labelled as so by the software.

If one omits the "drift/constant/conditional mean" parameter for an undifferenced model one is forcing the conditional mean to be 0.0 which can have deleterious consequences. This is akin to forcing a regression model through the origin.

The drift parameter is obtained while simultaneously estimating all parameters in the given model.

Wheres an optional drift parameter in a differenced model is an estimate of the period to period growth or stochastic "trend" which may or may not be significantly different from 0.0.

As a curious aside do you know a Mike Speakman from Warminster, Pa ?

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  • $\begingroup$ This was useful at one point. Don't know if all the issues are still true because it's old. stat.pitt.edu/stoffer/tsa4/Rissues.htm $\endgroup$ – mlofton Nov 4 '19 at 18:37
  • $\begingroup$ fundamentally they concurred with my akin statement $\endgroup$ – IrishStat Nov 4 '19 at 19:53
  • $\begingroup$ @IrishStat Thank you that is helpful. My data has an obvious linear trend and is stationary can you tell me what command would allow me to incorporate a linear trend? Unfortunately no I don't know a Mike Speakman. $\endgroup$ – Michael Howell Nov 4 '19 at 22:52
  • $\begingroup$ I don't think I can help you with actual commands ...all I can tell you is that when you assume a model as you are implying things can go very bad real quick !. $\endgroup$ – IrishStat Nov 5 '19 at 2:45
  • $\begingroup$ you say "an obvious linear trend and is stationary" . I say no . why don't you post the actual values ?... The original series may have trend while the residual series can be stationary . The assumption is that AFTER adjusting/filtering for consistent/predictable patterns the adjusted series (the residuals) should be stationary following no discernable pattern. $\endgroup$ – IrishStat Nov 5 '19 at 12:49

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