4.2 Consider the following two autoregressions in one dimension: (i) 6Xt 5Xt1 + Xt2 = ????t,...
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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
, ???? ∈ [−????, ????).
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