Dear Gretl Community,

I would like to know how to reproduce an automatic X-12-ARIMA specification inside Gretl. I'll try to explain better...

<hansl>
open fedstl.bin
data paynsa

smpl 2000:01
</hansl>

Using the GUI facilities to X-12-ARIMA (Menu -> Variable -> X-12-ARIMA Analysis) I get the following specification:

"Final automatic model choice : (0 2 1)(0 1 1)"

And I get the following model:

<model>
Estimation converged in   10 ARMA iterations,   31 function evaluations.
 ARIMA Model:  (0 2 1)(0 1 1)
   Nonseasonal differences: 2
   Seasonal differences:    1
                                              Standard
 Parameter                    Estimate          Errors
 -----------------------------------------------------
 Nonseasonal MA                                   
   Lag  1                       0.4834         0.06713

 Seasonal MA                                      
   Lag 12                       0.7977         0.05225
</model>

So I use it with the "arima" command:

<hansl>
arima 0 2 1 ; 0 1 1 ; paynsa --nc --x-12-arima
</hansl>

This gives me the following result:

<model>
Modelo 3: ARIMA, usando as observações 2000:01-2014:04 (T = 172)
Estimado usando X-12-ARIMA (Máxima verossimilhança exata)
Variável dependente: (1-L)^2(1-Ls) paynsa

             coeficiente   erro padrão      z       p-valor
  ----------------------------------------------------------
  theta_1     -0,545388     0,0619664     -8,801   1,35e-018 ***
  Theta_1     -0,789758     0,0506616    -15,59    8,66e-055 ***
</model>

How can I exactly reproduce the model estimated by the X-12-ARIMA procedure?

Best regards,
Henrique Coêlho de Andrade

Diretoria de Estratégia e Organização

Divisão de Cenários e Estudos Macroeconômicos

Banco do Brasil

henrique.andrade@bb.com.br