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2 (a) Let {Yt} be a weakly stationary process and let X, = B'l'}, where B is the backshift operator and r is a positive integer. Do {K} and {Xi} have the same ACVF'? If true, prove your answer. If false, give a counterexample. [2] (b) Let {K} be a weakly stationary process and let X, = VTYt, where V, is the lag r difference operator and 7' is a positive integer. Do {Yt} and {Xt} have the same ACVF? If true, prove your answer. If false, give a counterexample. [3] For parts (0) and (d) below, use the following notation and denitions. Let {Z3} be a zeromean WN(02) process and let {3,} be a seasonal component with period (1 2 2 (note that this implies that s, = c for all t, where c is a constant, is not allowed). Let W, = 3,;Zt. (c) Show that {Wt} is not stationary. [2] ((21) Suppose d is odd, say at = 2g + 1, where q is a positive integer. Also assume that 3.11 7E 0. Let X, = 2:10 st,_q+j. Show that {X,} is stationary and compute its ACVF and ACF. [8]