Consider the ARM A(1,1) process: Z4 = 024-1 + at - Dat-1; where o and are model parameters, and ai, a2, random variables with mean 0 and variance o?. are independent and identically distributed (8) (a) Under what conditions on o and 6 is the process both stationary and invertible? (b) Show that the autocorrelation function (ACF) of the process is: if k=0, Pk { 1 (1 - 0) (0-0) 1 - 206 +62 if k>1. (10) (c) If the respective estimates of the autocorrelations 21 and 22 are P1 = 0.523 and 22 = 0.418, show that the method of moments estimate of ois o = 0.7992 and that the method of moments estimate of is which solves the equation: 1 0.79926) (0.79 0.7992 2-0) -0) = 0.523 0.83608 +0.05236. Find the appropriate 0. (10) Consider the ARM A(1,1) process: Z4 = 024-1 + at - Dat-1; where o and are model parameters, and ai, a2, random variables with mean 0 and variance o?. are independent and identically distributed (8) (a) Under what conditions on o and 6 is the process both stationary and invertible? (b) Show that the autocorrelation function (ACF) of the process is: if k=0, Pk { 1 (1 - 0) (0-0) 1 - 206 +62 if k>1. (10) (c) If the respective estimates of the autocorrelations 21 and 22 are P1 = 0.523 and 22 = 0.418, show that the method of moments estimate of ois o = 0.7992 and that the method of moments estimate of is which solves the equation: 1 0.79926) (0.79 0.7992 2-0) -0) = 0.523 0.83608 +0.05236. Find the appropriate 0