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1 (a) Let X, = s2)+s3)+s4), where {39)}, {3533)}, and {831)}, are seasonal components with periods 2, 3, and 4, respectively. Find a linear lter {a0,a1,a2,a3,a4,a5} (i.e., a0, . . .,a5 are all nonzero and are the only nonzero coefcients of the lter) such that the output of the lter when applied to {Xt} is a constant for all t. [8] (b) Let d1 and d2 be positive integers, with d1 75 d2. Let {3911)} and {3312)} be seasonal components with periods d1 and d2, respectively. Let X, = sd13+3d and let Y, = leX,. For each of the following statements, say whether it is TRUE or FALSE. If TRUE prove the statement, and if FALSE give a counterexample. (i) lengt is a constant. [3] (ii) Vd1+d2Xt is a constant. [3] (ii) Vd2Y; is a constant. [3]