Dear all:

step one:

I use a set of data and select two appropriate ARIMA model (parameter is significant, and residual is white noise), they are ARIMA(1,1,0) and ARIMA(3,1,2).(their observations are different because lags of AR or MA are different).

step two:

I want to choose one from them by AIC and BIC. But there comes a question. In order to compare their AIC and BIC, I have to set the sample range of these two models the same (their observations are the same now). But the new ARIMA(1,1,0) and original ARIMA(1,1,0) are different models (for example, their parameters are different. Residual of original model is white noise but new model is not). The new ARIMA(3,1,2) and original ARIMA(3,1,2) are also different models. If AIC and BIC of new ARIMA(1,1,0) is lower than AIC and BIC of new ARIMA(3,1,2), which model should I select? New ARIMA(1,1,0) or original ARIMA(1,1,0)

p.s. Is there any wrong on the procedure of selection of ARIMA model? Should I set the sample range the same at start (step one)?

Thanks a lot.