Use R Code to solve the Problem

Question 2 (A) Suppoese Xt follows an AR(1) model: Xt = 0.9X1-1 +6, where = 0.5. Simulate an episode of Xt with 1 milon observations (Hint: Use the R command arima.sim) Calculate the first through 10th lag autocorrelations of the simulated series. Compare the estimated autocorrelations with the theoretical counterparts (Hint: the theoretical autocorrelations for AR(1) is - , where is the lag.) (B) Suppose Z XY, where X, is the same as in (A), and Y follows an AR(1) model: Yt-0.5,-1 + Et, where .-0.5. Is an AR (1) model appropriate to describe Zt? Question 2 (A) Suppoese Xt follows an AR(1) model: Xt = 0.9X1-1 +6, where = 0.5. Simulate an episode of Xt with 1 milon observations (Hint: Use the R command arima.sim) Calculate the first through 10th lag autocorrelations of the simulated series. Compare the estimated autocorrelations with the theoretical counterparts (Hint: the theoretical autocorrelations for AR(1) is - , where is the lag.) (B) Suppose Z XY, where X, is the same as in (A), and Y follows an AR(1) model: Yt-0.5,-1 + Et, where .-0.5. Is an AR (1) model appropriate to describe Zt