Problem 3 (20pts) Problem 3a. (10pts) Is the following AR(4) model stationary? (Justify your answer): r = 20 (1/90)r-1 + (1/30)r1-2 + (19/90)r:-3 (3/10)r2-4 + . Hint: compute the characteristic polynomal for the model, and compute its roots. Problem 3b. (10pts) Consider AR(2) model r, = 00 + 01ri-1 + $r-2 +, where {E1} is weak WN(0,0%). Assume that r, is weakly stationary. Calculate Er), Var(r) and Cou(ri,r1-1) for all t. Problem 3 (20pts) Problem 3a. (10pts) Is the following AR(4) model stationary? (Justify your answer): r = 20 (1/90)r-1 + (1/30)r1-2 + (19/90)r:-3 (3/10)r2-4 + . Hint: compute the characteristic polynomal for the model, and compute its roots. Problem 3b. (10pts) Consider AR(2) model r, = 00 + 01ri-1 + $r-2 +, where {E1} is weak WN(0,0%). Assume that r, is weakly stationary. Calculate Er), Var(r) and Cou(ri,r1-1) for all t