I have researched all over the text books and software (R/SAS/SPSS), but I have not encountered Simple Exponential Smoothing (SES) with a drift ?

Is it possible to add a drift term to Simple exponential smoothing, so that SES captures the direction of the trend? If yes, how is this implemented in software like forecast package in R or any other software?

Also, is SES with drift equivalent to ARIMA(0,1,1) + Drift ?


If the drift changes over time, then you can use double exponential smoothing known as the Holt-Winters procedure.

see: https://en.wikipedia.org/wiki/Exponential_smoothing#Double_exponential_smoothing

R has an implementation.

  1. The theta method of Assimakopoulos and Nikolopoulos (2000) is equivalent to simple exponential smoothing with drift. This is demonstrated in Hyndman and Billah (2003). This is already implemented in the forecast package in R.
  2. Yes. SES is equivalent to ARIMA(0,1,1), so adding constant with make them equivalent too.


  1. https://www.rdocumentation.org/packages/forecast/versions/8.1/topics/thetaf
  2. https://people.duke.edu/~rnau/411arim.htm#ses

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