hw6_solution

hw6_solution - PSTAT 174/274 HW#8 Solution 1(a Define Yt...

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Unformatted text preview: PSTAT 174/274 - HW #8 Solution 1. (a) Define Yt = (1 - B)Xt = t - t-1 + nt - nt-1 = Wt + nt - nt-1 2 2 w + 2n , h = 0 2 -n , h=1 Y (h) = 0, h2 1, h=0 2 n 1 Y (h) = h=1 - 2 2 = - 2+c , w +2n 0, h2 (b) Should be trivial. (c) If you set /(1 + 2 ) = -1/(2 + c) and solve for where || < 1, = 2. (a) At t = 2, we can find the linear system as X1 X2 = 1 -1 1 0 2 2 + n1 + w2 n2 1 2 (c2 + 4c)1/2 - c - 1. ^ With OLS estimation, you get 2 = [^2 , 2 ] = [x2 , x2 - x1 ] and ^ P2 = (b) Observation Eq: Xt Transition Eq: t ^ 3|2 P3|2 K3 e3 ^ 3 3. (a) Xt Xt-1 = 1 1 2 0 Xt-1 Xt-2 + 1 Wt . 0 = = 1 1 0 0 t t + n t = ht t + n t 2 n 2 n 2 2n 2 n 2 + w 1 = Gt t-1 1 t-1 2x2 - x1 x2 - x1 5 3 ^ = G3 2 = = G3 P2 G3 P3|2 h3 1 = = 2 h3 P3|2 h3 + n 6 ^ = x3 - h 3|2 3 ^ = 3|2 + K3 e3 = 5 1 1 6 x3 + 3 x2 - 6 x1 1 2 (x3 - x1 ) ...
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.

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