# [R] Re: Seasonal ARMA model

Ajay Shah ajayshah at mayin.org
Sun Jul 4 10:45:37 CEST 2004

```> It might clarify your thinking to note that a seasonal ARIMA model
> is just an ``ordinary'' ARIMA model with some coefficients
> constrained to be 0 in an efficient way.  E.g.  a seasonal AR(1) s =
> 4 model is the same as an ordinary (nonseasonal) AR(4) model with
> coefficients theta_1, theta_2, and theta_3 constrained to be 0.  You
> can get the same answer as from a seasonal model by using the
> ``fixed'' argument to arima.  E.g.:

set.seed(42)
x <- arima.sim(list(ar=c(0,0,0,0.5)),300)
f1 = arima(x,seasonal=list(order=c(1,0,0),period=4))
f2 = arima(x,order=c(4,0,0),fixed=c(0,0,0,NA,NA),transform.pars=FALSE)

Is there a convenient URL which shows the mathematics of the seasonal
ARMA model, as implemented by R?

I understand f2 fine. I understand that you are saying that f1 is just
an AR(4) with the lags 1,2,3 constrained to 0. But I'm unable to
generalise this. What would be the meaning of mixing up both order and
seasonal? E.g. what would it mean to do something like:

arima(x,order=c(2,0,0),seasonal=list(order=c(2,0,0),period=12))

--
Ajay Shah                                                   Consultant
ajayshah at mayin.org                      Department of Economic Affairs
http://www.mayin.org/ajayshah           Ministry of Finance, New Delhi

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