[Gretl-users] Single ARIMA Command with Seasonal Differences

[Allin Cottrell]

On Sun, 17 Feb 2008, Tom La Bone wrote:

> I have some quarterly data U1 (variable 1) I would like to model the data as
> an ARIMA process. I take the first difference of U1 to create d_U1 (variable
> 3) and then take the first difference of d_U1 to create d_d_U1 (variable 4).
> Finally, I take the seasonal difference to create sd_d_d_U1 (variable 5) and
> try an ARIMA(0,0,1) model. The Gretl commands are:
> 
>   diff U1
>   diff d_U1
>   sdiff d_d_U1
>   arima 0 0 1 ; 5 

On small point here: you can avoid "d_ pile-up" by nesting these 
functions:

genr Dy = sdiff(diff(diff(y)))

> 
> I would like to do all of this in one command. I have tried a number of
> different commands looking something like
> 
>   arima 0 2 1 ; 0 1 0 ; 1
> 
> but have been unable to get the same answers as I did doing the evaluation
> step-by-step. 

You're right, the second command above ought to produce the same 
results as the first, with the pre-differenced variable.

You have exposed a bug in the arima auto-differencing code, for 
the case d > 1 and D > 0.  This is now fixed in CVS and in
the current Windows snapshot, at

http://ricardo.ecn.wfu.edu/pub/gretl/gretl_install.exe

Allin Cottrell