Exercise 6.9.9. Let et be second-order stationary and define yt = s= asets and wt =
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Exercise 6.9.9. Let et be second-order stationary and define yt =
∞Σ
s=−∞
aset−s and wt =
∞Σ
r=−∞
bryt−r, where Σ∞s=−∞ |as| < ∞ and Σ∞r =−∞ |br| < ∞.
(a) Show that fw(ν) = |A(ν )|2|B(ν )|2 fe(ν ).
(b) Show that wt =
∞Σ
s=−∞
cset−s, where cs =
∞Σ
r=−∞
as−rbr .
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