AIC and SBC: You should only use AIC or SBC to compare models which involve the same transformation (if one is used) and the same degree of differencing. You will lose some credit if you use AIC or SBC to compare models involving different transformations or degrees of differencing. Also note: if you want to compare models using AIC or SBC, it is best to use METHOD=ML in the ESTIMATE statement. The other estimation methods only compute an approximation to the AIC or SBC. Warning Messages: If you try a model and there are warning messages in the SAS output indicating failure to converge or some such problem, you should try a different model. You will lose some credit if you choose a model which produces such warning messages (if there are other models which look reasonable which do NOT produce such messages). Non-significant terms: We usually use P-value < .05 as our standard for statistical significance. Terms which are NOT statistically significant are usually dropped from the model. Sometimes terms which are not quite significant (the P-value is close to but not less than .05) are retained in the model if there is some good reason to, e.g., if they lower the AIC or greatly improve the residual ACF. In your homework, if you retain any non-significant terms, you should give a good reason for doing so. If you neglect to state a good reason, you will lose some credit.