I have the following result from using auto.arima which includes an SMA term. I would like to hand calculate using the coefficients to get the value of 786.1291812. I am unsure, however, about how to use the SMA term.

Series: ts_train 
Regression with ARIMA(3,0,1)(0,1,1)[12] errors 

         ar1     ar2      ar3      ma1     sma1
      0.8919  0.1849  -0.3847  -0.6419  -0.6783 
s.e.  0.1072  0.0917   0.0680   0.0990   0.0847 

In Excel, I have the following:

$$=JAN2017+(AR1*(DEC2017-DEC2016))+(AR2*(NOV2017-NOV2016))+(AR3*(OCT2017-OCT2016))+(MA1*(DEC2017actual - DEC2017fitted)) + (SMA?) $$


closed as off-topic by Michael Chernick, kjetil b halvorsen, COOLSerdash, AdamO, jbowman May 16 '18 at 23:11

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  • $\begingroup$ @Tim sorry! I didn't mean for it to come across as a programming question. I'm really more so unsure about how/what the SMA term is in an ARIMA and how it would be used in a formula to calculate the next step forecast. Does my edits help? If not, please assist as I'd really like to understand how SMA fits in the larger picture of an ARIMA formula. $\endgroup$ – user2340706 May 15 '18 at 22:07
  • $\begingroup$ are you asking about the interpretation of sma1? $\endgroup$ – Taylor May 16 '18 at 16:04
  • $\begingroup$ @user2340706 perhaps your question should be about SMA. $\endgroup$ – AdamO May 16 '18 at 16:40
  • $\begingroup$ Thanks for the advice AdamO and Taylor. Yes it’s more about SMA so I reworded my title. $\endgroup$ – user2340706 May 17 '18 at 16:52

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