For the calculations below, it is useful if you have general expressions based on?and?A2before substituting in specific numbers.

For the calculations below, it is useful if you have general expressions based on and of before substituting in specific numbers. Suppose A, : t = 0, 1, .. . is a white noise (independent and identically distributed) sequence with mean 0 and variance of. Let Z, = A, + AH so that Z, is a MA(1) time series. Part a) If o-A = 3 and/3 = 0.3, then Var(Z,) is Part b) If a} = 3 and = 0.3, then Cov(Z,,Z,+1) is Part c) If 0A = 3 and}? = 0.3, then Cor(Z,,Z,+1) is Part d) If a} = 3 and = 0.3, then Cov(z,,z,+2) is Part e) Consider Cor(Z,, Z,+1) as a function of ,6 2 0. The maximum possible value of the correlation of lag 1 is: Part f) For the general expression for Cor(Z,, Z,+1) as a function of , check what happens when is replaced by 'l. Also che what happens when ,6 is replaced by