R help - Jul 2004 - Re: Seasonal ARMA model

> 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

On Sun, 4 Jul 2004, Ajay Shah wrote:
> > 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?
No, but there is a book, MASS4 (see the FAQ).  Although the software is in 
base R it was in fact written by me to support MASS4.

R follows S-PLUS in some of its choices of signs, which do differ between 
accounts.
> 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))
That is in MASS4 and most of the books referenced on the help page.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595