Monthly data for in-sample forecasting : sample from 1980M1 to 1990M12(the number of samples is 132)

Estimating the model:

The using observations of ARIMA(1,1,1) : 1980M3 to 1990M12. (number:130)

The using observations of ARIMA(2,1,0): 1980M4 to 1990M12. (number:129)

The using observations of ARIMA(1,1,0)(1,1,0)12: 1982M3 to 1990M12. (number:106)

 

Can I compare these three models by AIC or BIC?

 

In order to make the number of observations of these models the same for comparing AIC and BIC, I have to set the sample range from 1982M3 to 1990M12.

Estimating the model:

The using observations of ARIMA(1,1,1) : 1982M3 to 1990M12. (number:106)

The using observations of ARIMA(2,1,0): 1982M3 to 1990M12. (number:106)

The using observations of ARIMA(1,1,0)(1,1,0)12: 1982M3 to 1990M12. (number:106)

 

But now the period of in-sample forecasting is not 1980M1 - 1990M12.

The outcome of two ARIMA(1,1,0)(1,1,0)12 are the same.

The outcome of two ARIMA(1,1,1) are different.

The outcome of two ARIMA(2,1,0) are different.

 

My question is how to choose ARIMA model under in-sample forecasting period is 1980M1 -1990M12 . I want to use sample from 1980M1 to 1990M12 for in-sample forecasting. But in order to compare AIC and BIC, I have to set the sample range from 1982M3 to 1990M12. The outcome of ARIMA(1,1,1) and ARIMA(2,1,0) are different. How do I use the same data to choose ARIMA model from different order of AR and MA (SAR and SMA)?

Can I compare AIC and BIC under in-sample forecasting period is 1980M1 -1990M12 ?