Independent time series exam

Problem 6: Let Xt, t = 0, +1, 12, . . . and Yt, t = 0, +1, 12, . .. be two independent time series with means 0 and autocovariance r1 (h) and r2(h), respectively . That is Cov[Xt, Xith] = ri(h), Cov[Yt, Yrth] = 12(h) and cov[Xt, Ys] = 0 for all t, s, h, (in particular, Var[X, = r1(0)] and Var[Y,] = r2(0)). Consider the time series Zt = BoX+ + BYt,t = 0+1, 12,... , where Bo and B1 are nonrandom constants. (a) Find the mean and variance of Zt. (b) Find the autocovariance function of the time series { Zt, t = 0 + 1, 12, . . . }. (c) Is {Zt, t = 0 + 1, 12, . . . }. stationary?1. Let wt, -co