# [R] Re: Seasonal ARMA model

From: Ajay Shah <ajayshah_at_mayin.org>
Date: Sun 04 Jul 2004 - 18:45:37 EST

> 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@mayin.org                      Department of Economic Affairs
http://www.mayin.org/ajayshah           Ministry of Finance, New Delhi

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