Consider the time series { Zt } satisfying Z1 = a1; Zt = 0.2Zt-1 + at for t > 1. (a) By mathematical induction, show that Zt = _k 0 0.2kat-k. (b) Find the mean E(Zt) and the variance Var(Zt). (c) Find Cov( Zt, Zt-k ) for t > k and k > 0. Suppose Zt = 8+ 4t + 2Xt, where Xt is a zero-mean stationary series with autocovariance function 7k. (d) Find the mean and the autocovariance function of AZt = (1 - B) Zt. (e) Is AZt stationary? Why