For an AR model of order 2, yn = a1yn−1 + a2yn−2 + vn, vn ∼ N(0,σ 2 ); (1) Show the formula to obtain the autocovariance function C0,C1,... . (2) Show the expression to obtain the power spectrum...

For an AR model of order 2, yn = a1yn−1 + a2yn−2 + vn, vn ∼ N(0,σ 2 );

(1) Show the formula to obtain the autocovariance function C0,C1,... .

(2) Show the expression to obtain the power spectrum p(f), 0 ≤ f ≤ 1/2.

(3) Obtain C0, C1, C2 when a1 = 0.8, a2 = −0.6 and σ 2 = 1.

(4) For the same case, obtain the expression for the power spectrum p(f). Investigate for which frequency f , p(f) attains its maximum.