 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-47/2/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

(1 - B^{12}) (1 - B)

, with

B

Z_{t} = X_{t} - X_{t - 1} - X_{t - 12} + X_{t - 13},

and its only nonzero coefficients are

c_{0} = 1

c_{1} = - 1

c_{12} = - 1

c_{13} = 1

G_{c} (λ) = 4 sin (λ /2) ∣ sin (6 λ) ∣, 0 \leq λ \leq π .

f_{Z} = 16 sin^{2} (λ /2) sin^{2} (6 λ) f_{X}

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