Exercise 6.9.9. Let et be second-order stationary and define yt = s= asets and wt = r= brytr, where s= |as| <

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 .