Sam,
Monthly data for in-sample forecasting : sample from 1980M1 to
1990M12(the number of samples is 132)
Estimating the model:
Is 1980M1 the start of your data? If so, there's no way to estimate all of these
different models AND have your "in-sample forecasting" period begin then, since
you'll lose different numbers of observations due to lags and differencing.
Can I compare these three models by AIC or BIC?
Sure, but you
should compare them over the same number of observations
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.
<snip>
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.
See above.
PS