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

Rolf Turner r.turner at auckland.ac.nz
Wed Jun 21 02:36:07 CEST 2017

```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]

(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

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

```