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

[Rolf Turner]

On 20/06/17 17:21, Y S wrote:
> 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
> Call:
> arima(x = koeps, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 4))
> Coefficients:
>            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
> 
> Thanks!

Please do not post in html, although this doesn't seem to have messed 
things up too badly in this instance.

The help for arima() says:

> The definition used here has
> 
> X[t] = a[1]X[t-1] + … + a[p]X[t-p] + e[t] + b[1]e[t-1] + … + b[q]e[t-q]

so your first possibility, i.e.

(1-B)(1-B^4) X_t=(1-0.4096B)(1-0.8203B^4) a_t

is the correct one.

This stuff *does* get confusing; parity errors keep creeping in!

cheers,

Rolf Turner

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