(Bonus: 10 points) Let { , } be a weakly stationary time series. Define = 1 + 21 + + +1for , where 1, 2, ... , are any constants. Show that the time series { , } is weakly stationary.

(Bonus: 10 points) Let {Yt, t E Z} be a weakly stationary time series. Define Xt = C1Yt + C2Yt-1 + ... + CKYt-k+1fort E Z, where c1, C2, ..., Ck are any constants. Show that the time series {Xt, t E Z} is weakly stationary