PMActuary, the derivation on p.56 is for the particular case when all summands are positive. In our HW we have alternating signs, so we have to do a different calculation.
Basically, due to alternating signs, the terms in the covariance sum will enter one with +, the other with -, like this:
for the term -phi^2 x e(t-2) the other one will be +phi x e(t-2), and so on.
(However, the term e(t-1) enters both times with +).
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