2.3 Let Xt be a stationary AR(2) process X = c +bXt1 +b2Xt2+ t, (a) Show...

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2.3 Let Xt be a stationary AR(2) process X = c +bXt1 +b2Xt2+ t, (a) Show that the ACF of Xt satisfies: p(k) = bp(k 1) + b2p(k 2) for all values of k > 0. (b) Use part (a) to show that (b1, b2) solves the following system of equations: p(1) (21)) - (1) "")) (62) (c) If p(1) = 0.4 and p(2) = 0.2. Find b1, b2 and p(3). 1 (d) If we estimate p(1) and (2) by their sample ACF (1) and (2), can we then estimate b1, b2? (This is a different way to estimate b, b2 than using MLE as we covered in the class). 2.3 Let Xt be a stationary AR(2) process X = c +bXt1 +b2Xt2+ t, (a) Show that the ACF of Xt satisfies: p(k) = bp(k 1) + b2p(k 2) for all values of k > 0. (b) Use part (a) to show that (b1, b2) solves the following system of equations: p(1) (21)) - (1) "")) (62) (c) If p(1) = 0.4 and p(2) = 0.2. Find b1, b2 and p(3). 1 (d) If we estimate p(1) and (2) by their sample ACF (1) and (2), can we then estimate b1, b2? (This is a different way to estimate b, b2 than using MLE as we covered in the class).