HW4_Solutions - Solutions to HW 4 Exercise 5.1 X t +1 = Z t...

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Solutions to HW 4 Exercise 5.1 11 1 1 1 ˆ , ( | , ,...) tt t t t t t t X ZZ X E X X X Z θ ++ + + =+ = = ˆ ( | , ,...) 0, 2 th t t XZ Z XE X X X h + + + = = () 2 111 1 22 1 ˆ Var( ) ˆ Var( ) 1 , 2 ttt t t h eXXZ e Z e h σ θσ +++ + + + + + =−= = + 1 t Exercise 5.2 1 1 1 ˆ , ( | , ,...) t t t t t X X E X X X X φ + + = = 2 21 2 2 2 1 1 12 1 ˆˆ , ( | , ,...) , ( | , ,...) φφ + + + + + + + + = == = t t t t t t h t t t t 1 t X X E XX X X X X X E X X X X X 2 2 ( 1 ) 1 2 2 1 ˆ Var( ) 1 ... 1 1 σφ −− + + + + + + + ⎛⎞ + + = = = ⎜⎟ ⎝⎠ hh h t t t t nh n hk eXX X X Z a ea a 1 ˆ ˆ ˆ t h t h t t t XXZ YX Y Y X Y Y X μ φμ μφ μμ + + + −= − + =− = = + = + = + Problem 1 ( ) 4 1 ˆ(1)~ N (1), 1 3 (1) 4 = N (.5676) nn ρρ ρ ⎡⎤ −+ ⎣⎦ & , ( ) 1 ˆ(2) ~ N 0, 1 2 =N 0, (1.389) + & . If .6 = , then 2 .6 .4412 . 3 6 = , (2) 0 = . ˆ 95% CI: (1) 1.96 .005676 .432 .148 (.284, .580) ± =±= . ˆ 95% CI: (2) 1.96 .01389 .145 .231 ( .086, .376) ±= ± = . Both CIs contain the values of the parameters (.4412 and 0, respectively), therefore “Yes”.
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.

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