[R] How to write an estimated seasonal ARIMA model from R output?

Y S nyshaw at outlook.com
Tue Jun 20 07:21:14 CEST 2017

I'm trying to use the following command.
arima (x, order = c(p,d,q), seasonal =list(order=c(P,D,Q), period=s)

How can I write an estimated seasonal ARIMA model from the outputs. To be specifically, which sign to use? I know R uses a different signs from S plus.

Is it correct that the model is:
(1-ar1*B-ar2*B^2-...)(1-sar1*B^s-sar2*B^2s-....)(1-B)^d(1-B^s)^D X_t=(1+ma1*B+ma2*B^2+...)(1+sma1*B^s+sma2*B^2s+....) a_t

For example:
> m1=arima(koeps,order=c(0,1,1),seasonal=list(order=c(0,1,1),period=4))
> m1
arima(x = koeps, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 4))
          ma1     sma1
      -0.4096  -0.8203
s.e.   0.0866   0.0743

Should the estimated model be written as:
(1-B)(1-B^4) X_t=(1-0.4096B)(1-0.8203B^4) a_t
or (1-B)(1-B^4) X_t=(1+0.4096B)(1+0.8203B^4) a_t


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