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,...

For the calculations below, it is useful if you have general expressions based on fl 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. LetZ, = A, + flAH 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 fl = 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 fl = 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 fl, check what happens when fl is replaced by fl‘l. Also chewhat happens when ,6 is replaced by —fi