[Gretl-devel] ARMAX and diffs

[Ignacio Diaz-Emparanza]

I was trying to estimate an ARIMA model with a intervention (a level shift). 
I identificated a ARIMA(0,1,1) model for the data previous to the 
intervention, so I tried to estimate:

Yt=w*St+[(1-\theta L)/(1-L)]*ut

St is a step variable, with value 1 after 2002:02 and 0 before that (I know 
the intervention should be a gradual shift, but this is easier to explain).
The problem is that I have no very clear, based on the gretl manual, how gretl 
treat the difference with the explanatory St variable. So I did some tryings
and found what I think is an inconsistency in the treatment of the explanatory 
variable.

Differencing the previous equation I obtain:

d_Yt=w*Pt+(1-\theta L)*ut

where Pt=(1-L)*St. 

In the following script I firstly estimate  this equation with the data in the 
attached file. The two following equations estimate the model in levels, but 
it seems that the gretl native command does not use the St variable as 
the --x12-arima, because the results are very different. I seems that gretl 
is not differencing the St variable. I do that manually in the last command 
and the results now seems consistent with that of X12arima and that obtained 
with the first command.

<script>
open import-NE.gdt
arima 0 0 1 ; d_Y P 0
arima 0 1 1 ; Y S 0
arima 0 1 1 ; Y S 0 --x-12-arima
arima 0 1 1 ; Y P 0
</script>

Could you, Allin or Jack, please correct this behaviour?
Thanks.









-- 
Ignacio Diaz-Emparanza  
DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA)                                        
UPV/EHU
Avda. Lehendakari Aguirre, 83 | 48015 BILBAO
T.: +34 946013732 | F.: +34 946013754
www.et.bs.ehu.es 
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