11. Consider the MA(2) model ????j = −b2wj−2 − b1wj−1 + wj with invertibility conditions

(i) b1 + b2 < 1, (ii) b2 − b1 < 1, and (iii)

|

b2|

< 1.

Pick choices of b1 and b2 that violate each condition, but only one condition at a time. In each case, show b(B) = 0 has one or more roots inside the unit circle.

Since b(B) = 0 is a quadratic, it should be possible to do this easily.