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1.32 Let { xt; t = 0, +1, +2, ...} be iid(0, o-2). (a) For h 2 1 and k 2 1, show that X Xt+h and Xs*s+k are uncorrelated for all s # t. (b) For fixed h 2 1, show that the h X 1 vector n o-2n-1/2 > ( xX + 1 , ..., XAXith )' - ( 21, ..., In)' t= 1 where z1, . .., Zh are iid N(0, 1) random variables. [Hint: Use the Cramer-Wold device.] (c) Show, for each h 2 1, n-h n-1/2 M Xt Xtth [ (x - F ) ( With - 5 ) 40 as n - oo t = 1 t= 1 where x = n- 21-1 (d) Noting that n-1 Er_, x? -> 02 by the WLLN, conclude that n'/2 [p(1), . .., p(h)]' -> (z1, ..., Zh)' where p(h) is the sample ACF of the data X1, . . ., Xn