Let {Xt} be the AR(1) process Xt = QXt-1+Zt where { Zt} ~ WN(0, o?). Let {Yt} be Yt = Xt + Wt where {Wt} ~ WN(0, 2). Assume E(Ws Zt) = 0 for all s and t. 5. Show that {Yt} is stationary and find its ACVF. 6. Define another times series {Xt} Ut = Yt - qYt-1. Show that {Ut} is 1-correlated, and hence, is MA(1) process. (Hint) Use Proposition 2.1.1. 7. From the previous result, conclude that {Yt} is an ARMA(1,1) process. Express {Yt} as a form of ARMA(1,1), that is, fill ( ) in the following: Yt - QYt-1 = ( )