4. Consider the ARMA(2,1) process Xi - aX -2 = Z - BZ -1, where a, 8 are real and a, 3 0,a # 8. (a) Under which conditions is the process X, stationary (5 ponts) and invertible (5 points)? (b) Given the observations X1,...,Xn, what is your best prediction for Xn+1 and Xn+2 at the forecast origin Xn (4 points)? What is the corresponding forecasting error (6 points)? (c) Compute its autocovariance functions 70), 7(1) and 7(2) (15 points)? What are the values of p(1) and p(2) (5 points)? 4. Consider the ARMA(2,1) process Xi - aX -2 = Z - BZ -1, where a, 8 are real and a, 3 0,a # 8. (a) Under which conditions is the process X, stationary (5 ponts) and invertible (5 points)? (b) Given the observations X1,...,Xn, what is your best prediction for Xn+1 and Xn+2 at the forecast origin Xn (4 points)? What is the corresponding forecasting error (6 points)? (c) Compute its autocovariance functions 70), 7(1) and 7(2) (15 points)? What are the values of p(1) and p(2) (5 points)