# Multiplicative / Factored ARIMA Models

I have been working on transitioning from SAS to R and am stuck on how to replicate a multiplicative (or factored) ARIMA model in R. I have yet to see anything online or in documentation that would allow me to do this.

In SAS, an AR model would be subset/additive if p=(2, 8, 9) and would multiplicative if I said p=(2)(8)(9).
(see pp 206-7 https://support.sas.com/documentation/onlinedoc/ets/132/arima.pdf)

In R, I have only seen how to replicate an additive model. Taking the example above, an additive model would look like this in R:

``````ar<-data%>%
model(ar=ARIMA(y ~ 0 + x1 + x2
+pdq(9,1,0, fixed=list(ar1=0, ar2=NA, ar3=0, ar4=0, ar5=0, ar6=0, ar7=0, ar8=NA, ar9=NA))
+PDQ(0,0,0), method="ML"))
``````

I am wondering how I could run a multiplicative / factored model?
Would be grateful for any advice!

The SAS example given addressed a model that "multiplies" two models, one of which is annually lagged, hence "factored", to account for seasonalityâ€”annual in the example given. The general model for combining these two aspects is X-13ARIMA-SEATS. An `R` implementation is provided in the x13binary package, with seasonal providing an R interface and seasonalview providing a GUI. An alternative interface is provided by x12.

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Thank you! I will look into these!

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