Question: please answer (3) Consider the MA(1) process Xn = Zn + 0Zn-1, Zn ~ N(0, 1), (a) Use the Durbin-Levinson algorithm to find the best

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(3) Consider the MA(1) process Xn = Zn + 0Zn-1, Zn ~ N(0, 1), (a) Use the Durbin-Levinson algorithm to find the best linear predictor Xn+1 = 03,1Xn + 03,2Xn-1 + 03,3Xn-2 (b) Find the partial autocovariance function a(1), a(2) and a(3). (c) Use mathematical induction to prove that an, 1 = (-0) -(2-1) ( 1 + 02 + ... + 02n-2) an,n an, n = - ( - 0) n/ (1 + 02 + ... + 0 2n)

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