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.]

If your original series is stationary then you can regress on original y(t)'s.  But if you need to first difference your series in order to obtain stationarity, then I believe you'll need to regress against the first-differenced values.  AR(2) is similar to AR(1), your Y values are the, well, Y values, and your X values are your Y values lagged 2 periods, I think.