A4 soln - STA4005B Assignment 4(Solution) 1) 3 2 1 4 . 4 ....

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Unformatted text preview: STA4005B Assignment 4(Solution) 1) 3 2 1 4 . 4 . 4 . − − − + − − = t t t t t a a a a Z , , , 2 48 . 1 a σ γ = 2 1 4 . a σ γ − = 2 2 56 . a σ γ − = 2 3 4 . a σ γ = 37 / 10 1 − = ρ , 37 / 14 2 − = ρ , 37 / 10 3 = ρ 27027 . 1 11 − = = ρ φ , 4870 . 1 2 1 2 1 2 22 − = − − = ρ ρ ρ φ , 01898 . 2 2 1 2 2 1 2 2 2 2 1 3 2 1 2 1 3 1 2 2 1 3 33 − = − − + − − + + = ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ φ 2) 1 1 − − − = − t t t t a a Z Z θ t t a B Z B ) 1 ( ) 1 ( θ − = − t t a Z B B = − − − ) 1 ( ) 1 ( 1 θ t t a Z B B B = − + + + ) 1 )( 1 ( 2 2 L θ θ t t a Z B B B = − − − − − − − ) ) 1 ( ) 1 ( ) 1 ( 1 ( 3 2 2 L θ θ θ θ θ t t i i i a Z B = − − ∑ ∞ = + ) ) 1 ( 1 ( 1 θ θ t t t t j j t j t t i t i i t a Z Z a Z Z a Z B Z + = + − = + − = − ∞ = − − ∞ = + ∑ ∑ ) ( ) )( 1 ( ) ) 1 ( ( 1 1 1 1 λ θ θ θ θ 3) Since for , there is no high sample autocorrelation as high lag (says k = 10). Thus a stationary = 10)....
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A4 soln - STA4005B Assignment 4(Solution) 1) 3 2 1 4 . 4 ....

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