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).
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.
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