Yeah. I see the issue. The summary (Ch13 p45) is an ARMA not an AR and that is the difference between the 2 questions. The approach for the AR one in the assignment is what I would do.
For the ARMA I can see the logic (so we have corresponding terms in the X and e vectors on the RHS) but you could also write it as:
\(\pmatrix{X_t \\ X_{t-1}} = \pmatrix{\alpha_1 & \alpha_2 \\ 1 & 0} \pmatrix{X_{t-1} \\ X_{t-2}} + \pmatrix{1 & \beta \\ 0 & 0} \pmatrix{e_t \\ e_{t-1}} \)
Last edited: Sep 26, 2016