4.2 Consider the following two autoregressions in one dimension:

(i) 6Xt − 5Xt−1 + Xt−2 = ????t,

(ii) 2Xt − 7Xt−1 + 3Xt−2 = ????t, where in each case {????t} is a white noise process with mean 0, variance 1.

(a) Show that the spectral density for the two autoregressions is given by the same function f(????)=(2????)

−1

|(2 − ei????)(3 − ei????)|

−2

, ???? ∈ [−????, ????).