(b) The 1st autocovariance is The 2nd autocovariance is (c) The 1st autocorrelation is The 2nd autocorrelation is (d) The conditional expectation of given YT is      2.5 0.7YT 2.5 0.7 102.3 74.11.  0      0  14.9. (a) E(Yt) E(et) b1E(et–1) bqE(et–q) [because E(et) 0 for all values of t]. (b)   where the final equality follows from var(et) for all t and cov(et, ei) 0 for i t.  0       0    (c) Yt et b1et–1 b2et – 2 bqet – q and Yt–j et – j b1et – 1 – j b2et – 2 – j     bqet – q – j and cov(Yt, Yt – j) where b0 1. Notice that  cov(et–k, et–j–m) 0 for all terms in the sum.  (d) and for j 1.   0  1(Yt   14.11. Write the model as Yt Yt – 1 – 1 Yt – 2) ut. Rearranging yields  0   1)Yt  1Yt  Yt (1 – 1 – 2 ut.
(b) The 1st autocovariance is The 2nd autocovariance is (c) The 1st autocorrelation is The 2nd autocorrelation is (d) The conditional expectation of given YT is  2.5  0.7YT  2.5  0.7 102.3  74.11. 14.9. (a) E(Yt)  0  E(et)  b1E(et–1)   bqE(et–q)  0 [because E(et)  0 for all values of t]. (b) where the final equality follows from var(et)  for all t and cov(et, ei)  0 for i t. (c) Yt  0  et  b1et–1  b2et – 2   bqet – q and Yt–j  0  et – j  b1et – 1 – j  b2et – 2 – j   bqet – q – j and cov(Yt, Yt – j)  where b0  1. Notice that cov(et–k, et–j–m)  0 for all terms in the sum. (d) and for j  1. 14.11. Write the model as Yt  Yt – 1  0  1(Yt – 1  Yt – 2)  ut. Rearranging yields Yt  0  (1  1)Yt – 1  1Yt – 2  ut.
sw3_exeol_oddonly.docx