It is a time series question. Thanks!

Question 1 [26 marks]. Consider the following MA(2) process 1 X: = Z: + alztl + EZH, where 61 7 0 is a constant and {Zt} is a Gaussian white noise process with mean 0 and variance 1. (a) Why do we require our weakly stationary models to be invertible? Explain the reason. [2] (b) Let p(-) be the autocorrelation function (ACF) for the MA(2) process above. Suppose p(1) = % and p(2) = 1%. Find the value of61. ['7] (c) Based on the 61 value computed in (b), determine whether the MA(2) process above is invertible. [4] ((1) Using the value of 61 computed in (b), calculate the variance of the sample mean (X1 +X2+X3+X4)/4. [13]