# Interpreting and calculating SMA [closed]

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

Coefficients:
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, jbowmanMay 16 '18 at 23:11

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• @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. – user2340706 May 15 '18 at 22:07
• are you asking about the interpretation of sma1? – Taylor May 16 '18 at 16:04