Should I be trying to replicate the NEAS results?

[NEAS: This is an independent student project. The NEAS postings are suggestions to get you started. You can construct an ARIMA model, compare two or more models for a given era, compare two or three eras by type of model of by model parameters, examine seasonality, test out-of-sample forecasts, and many other items.]

I've seen a few project samples where students compare the autocorrelation of a specified AR(p) model to the sample ACF for the time series with K values . If I understand correctly, the model autocorrelation is just the correlation between the predicted values specified by the model at lags 1 to (K-p). As such, the predicted series would actually correspond with terms 2 through term K of the original time series. My question is whether the autocorrelation of the model should be compared to the original time series sample acf or with a modifed version of the sample acf that omits the first p terms of the original time series?

[NEAS: Your question is good. Comparing with the original time series says: does the model represent the empirical data? Omitting the first p terms says: does the model predict well? In most cases, we ask the first question, so we compare with the original time series.]